Method and apparatus for monitoring cross-sectional shape of a pattern formed on a semiconductor device

ABSTRACT

A method is provided for estimating a cross-sectional shape or for monitoring manufacturing process parameters of a semiconductor device pattern to be measured. In this method, in order to enable SEM-based management of the cross-sectional shape or manufacturing process parameters of the pattern to be measured, the association between the cross-sectional shape or process parameters of the pattern and SEM image characteristic quantities effective for estimating the cross-sectional shape or process parameters of the pattern, is saved as learning data, and then the image characteristic quantities that have been calculated from a SEM image of the pattern are collated with the learning data to estimate the cross-sectional shape or to monitor process parameters of the pattern. Estimation with high accuracy and reliability is achievable by calculating all or part of three kinds of reliability (reliability of the image characteristic quantities, reliability of estimation engines, and reliability of estimating results) based on the distribution of the image characteristic quantities and judging from the calculated reliability whether additional learning of the learning data is necessary, or selecting and adjusting image characteristic quantities and estimation engine based on the reliability.

BACKGROUND OF THE INVENTION

The present invention relates generally to methods and systems forsemiconductor-manufacturing process estimating intended to evaluate andmanage circuit patterns formed on semiconductor wafers. Moreparticularly, the invention relates to a method and apparatus forestimating a cross-sectional shape of a pattern using a SEM image.

The characteristics of conventional transistor devices depend primarilyon the width of gate wiring (gate length), and duringsemiconductor-manufacturing processes, the width of pattern wiring hasbeen mainly measured and managed using critical-dimension scanningelectron microscopy (CD-SEM). However, as the formation offiner-structured semiconductor circuit patterns accelerated the tendencytowards shorter channeling of transistors, the cross-sectional shapes ofthe semiconductor patterns have become more important as one of majorinfluential factors upon the transistor device characteristics, inaddition to the above-mentioned wiring width.

Japanese Patent Laid-Open No. Hei 10-125749 describes an inspectionapparatus for semiconductor products and a method for manufacturing asemiconductor product, which are intended to determine the acceptabilityof processed patterns formed on a surface to be processed, by matchingparameters, combining a simulated three-dimensional geometric model(ideal image) and the three-dimensional image data acquired from thesurface to be processed, displaying the combined image on a displayscreen, and conducting evaluations based on display results.

SUMMARY OF THE INVENTION

With decrease in design margins along with the miniaturization and highdensity of LSI chips, appropriate management of patterns formed during asemiconductor manufacturing process becomes impossible only withconventional dimension management. Under these circumstances, it isbeing demanded that cross-sectional shapes of patterns formed be managedin addition to two-dimensional management.

However, it has been difficult to evaluate and manage variouscross-sectional shapes with a conventional CD-SEM, since theconventional technique has been used primarily for measuringtwo-dimensional shapes from a vertical direction (from above the wafervertically), such as wiring pattern line widths and contact holediameters.

In addition, the evaluation and management of various cross-sectionalshapes have presented the following problems:

(1) It has been difficult to measure the cross-sectional shapes offormed patterns or part or all of pattern-forming process parametersbased on a SEM image acquired from the top-down (vertical) direction(hereinafter, this image is called “top-down SEM image”).

(2) There has not been a method of judging the acceptability of a formedpattern based on its cross-sectional shape or from its process parametermeasurement results.

(3) There has not been a method for calculating, if a pattern to beformed is defective, data for adjusting the process parameters used in aprocess causing defects in the formation of the pattern and feeding thecalculated data back to the process site.

An object of the present invention is to provide a method and apparatusfor estimating cross-sectional shapes of patterns formed on asemiconductor device, the method and apparatus being adapted such that across-sectional shape of a pattern to be measured, or all or part ofassociated process parameters can be managed using a SEM, with highthroughput, and without damaging the pattern.

Another object of the present invention is to provide a method andapparatus for estimating cross-sectional shapes of patterns formed on asemiconductor device, the method and apparatus being adapted to enableadvanced process management with a SEM or the like by estimating across-sectional shape or process parameters of a pattern to be measuredto determine the acceptability of the pattern to be measured based onthe estimation results, or by calculating deviations from appropriatedata (specification values) and feeding data for adjusting the processparameters back to a process site such as an exposure process site,etching process site, or exposure mask design site, as required.

The present invention attains the above objects by providing a methodand apparatus for estimating a cross-sectional shape of a pattern formedon a semiconductor device, the method and apparatus featuring thefollowing:

In one aspect of the present invention relating to a method andapparatus for estimating a cross-sectional shape of a pattern formed ona semiconductor device, in order to judge whether sufficient estimationaccuracy can be obtained in estimated fluctuation ranges of variousparameters used for estimation, the invention presents the number oflearning data samples or a distribution state thereof to a user asrequired, calculates at least one index value (reliability) intended toevaluate the number of learning data samples or the distribution statethereof, and further presents the calculated index value (reliability)to the user as required. The index value is obtained by analyzing adistribution state of image characteristic quantities for changes in thecross-sectional shape or process parameters of the pattern, against theestimated fluctuation ranges of the parameters to be estimated, andquantifying the distribution in various terms such as density,continuity, and variance, in contrast to the acquired learning data, forexample. The index value is hereinafter called “reliability of the imagecharacteristics quantities.”

The apparatus for estimating a cross-sectional shape of a patternaccording to the present invention is constructed to include: learningmeans to collect learning data which includes SEM images of patternseach having various cross-sectional shapes and select an estimationengine for estimating the cross-sectional shape of each pattern; andperformance processing means to process a SEM image acquired from SEMthat images of the pattern on a sample (semiconductor wafer), calculatea characteristic quantity of the SEM image, conduct necessary processingwith the selected estimation engine, and estimate the cross-sectionalshape of the pattern on the sample. The performance processing meansincludes an output unit that outputs information on the estimatedcross-sectional shape of the pattern on the sample, together withinformation on reliability of the estimation results.

In addition, in the present invention, the apparatus having the aboveconstruction is used to conduct the learning process step of collectingthe learning data which includes the SEM images of the patterns eachhaving various cross-sectional shapes, and selecting the estimationengine for estimating the cross-sectional shape of each pattern, and theperformance process step of processing the SEM image acquired from SEMimaging of the pattern on the sample, calculating the characteristicquantity of the SEM image, conducting necessary processing with theselected estimation engine, and estimating the cross-sectional shape ofthe pattern on the sample, and generating in the performance processstep an output of the information relating to the estimatedcross-sectional shape of the pattern on the sample, together with theinformation on reliability of the estimation results.

In another aspect of the present invention relating to a method andapparatus for estimating a cross-sectional shape of a pattern of asemiconductor device in accordance with a SEM image obtained from thepattern formed on a sample using a CD-SEM through a requiredmanufacturing process for the semiconductor device during manufacturingprocesses, the invention is adapted to include a learning process stepand a performance process step. The learning process step includes: alearning data registration substep for collecting a first SEM imagegroup of a first pattern group of various cross-sectional shapesbeforehand as a learning sample using the CD-SEM, further collecting afirst cross-sectional shape information group of the first pattern groupusing another measurement apparatus, and thus registering a relationshipbetween the collected first SEM image group and the collected firstcross-sectional shape information group as learning data in a database;an image characteristic quantity calculation substep for calculating afirst distribution group of image characteristic quantities correlatedto three-dimensional geometric changes in the first pattern group, fromthe first SEM image group within the learning data registered in thelearning data registration substep; a reliability calculation substepfor calculating, based on the first distribution group of imagecharacteristic quantities within estimated fluctuation ranges of thecross-sectional shapes, calculated in the image characteristic quantitycalculation substep in the manufacturing process, one or a plurality ofreliability of the first image characteristic quantity group in thelearning data, reliability of a first estimation engine group forestimating the cross-sectional shapes or a process parameter group, andreliability of a first estimation results group on the cross-sectionalshape group estimated using the first estimation engine group; and adetermination substep for determining the learning data and a firstestimation engine on the basis of the reliability value or pluralreliability values calculated in the reliability calculation substep toregister the learning data and the first estimation engine in thedatabase. The performance process step includes: a SEM image acquisitionsubstep for acquiring a SEM image of the pattern to be measured; animage characteristic quantity calculation substep for calculating animage characteristic quantity from the SEM image of the pattern to bemeasured; a estimating substep for estimating a cross-sectional shape ofthe pattern to be measured in accordance with both the imagecharacteristic quantity calculated in the image characteristic quantitycalculation substep, and the learning data and first estimation enginedetermined in the determination substep; and a reliability calculationsubstep for calculating reliability of the estimation results obtainedin the estimating substep.

In another aspect of the present invention relating to a method andsystem for semiconductor-manufacturing process monitoring intended forpattern-forming process parameter estimation based on a SEM imageobtained from CD-SEM observation of a pattern formed on a sample througha required manufacturing process during manufacturing processes for asemiconductor device, the invention is adapted to include a learningprocess step and a performance process step. The learning process stepincludes: a learning data registration substep for collecting a secondSEM image group of a second pattern group formed using various processparameters using the CD-SEM as a learning sample beforehand, furthercollecting a second cross-sectional shape information group of thesecond pattern group using another measurement apparatus, andregistering a relationship between the collected second SEM image groupand the collected second cross-sectional shape information group aslearning data in a database; an image characteristic quantitycalculation substep for calculating a second distribution group of imagecharacteristic quantities correlated to three-dimensional geometricchanges in the second pattern group, from the second SEM image groupwithin the learning data registered in the learning data registrationsubstep; a reliability calculation substep for calculating, based on thesecond distribution group of image characteristic quantities withinestimated fluctuation ranges of the process parameters, calculated inthe image characteristic quantity calculation substep in themanufacturing process, one or a plurality of reliability of the secondimage characteristic quantity group in the learning data, reliability ofa second estimation engine group for estimating the process parameters,and reliability of a second group of estimation results on the processparameters estimated using the second estimation engine group; and adetermination substep for determining the learning data and a secondestimation engine on the basis of the reliability value or pluralreliability values calculated in the reliability calculation substep.The performance process step includes: a SEM image acquisition substepfor acquiring a SEM image of the pattern to be measured; an imagecharacteristic quantity calculation substep for calculating an imagecharacteristic quantity from the SEM image of the pattern to bemeasured; a estimating substep for estimating a process parameter of thepattern to be measured, in accordance with both the image characteristicquantity calculated in the image characteristic quantity calculationsubstep, and the learning data and second estimation engine determinedin the determination substep; and a reliability calculation substep forcalculating reliability of the estimation results obtained in theestimating substep.

According to the present invention, during process management with alearning-type engine to estimate a cross-sectional shape or processparameters of the pattern to be measured, it is possible to calculatethe above-mentioned reliability for judging whether the above-mentionednumber of learning data samples or the above-mentioned distributionstate is appropriate for obtaining sufficient estimation accuracy withrespect to estimated fluctuation ranges of the parameters used forestimation. It is also possible to present the reliability to a user andprompt the user to perform additional learning as required. In addition,when additional learning is necessary, it is possible to conductestimation with high accuracy and high reliability by providingnecessary samples for additional learning to the user and prompting theuser to perform additional learning.

Furthermore, according to the present invention, it is possible toprovide the user with reliability that is a reference value to selectimage characteristic quantities used for estimating cross-sectionalshapes or process parameters, select estimation engines, and adjust aweight between the image characteristic quantities or adjust a weightbetween the estimation engines so that the user can use the reliabilityto conduct appropriate selections or weight adjustments for theparticular subject to be estimated. Thus, highly accurate and highlyreliable estimation becomes possible.

These and other objects, features, and advantages of the invention willbe apparent from the following more particular description of preferredembodiments of the invention, as illustrated in the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic configuration diagram of a scanning electronmicroscope, FIG. 1B is a diagram that explains irradiation of asemiconductor wafer with electron beams, and FIG. 1C is a diagram thatshows pixels of an image obtained from detection of electrons emittedfrom the semiconductor wafer during the irradiation thereof with theelectron beams;

FIG. 2A is a diagram showing an example of the cross-sectional shapethat is typically considered to be most desirable, FIG. 2B is a diagramshowing a shape of a forward tapered pattern, and FIG. 2C is a diagramshowing a shape of an inverse tapered pattern, FIG. 2D is a diagramshowing a pattern shape called “bowing”, FIG. 2E is a diagram showing apattern shape that is round at upper corners, FIG. 2F is a diagramshowing a pattern shape that is protuberant at upper corners, FIG. 2G isa diagram that shows a pattern having a skirt shape at bottom, FIG. 2His a diagram that shows a pattern having portions called “notches” incross section, FIG. 2I is a diagram showing a thinned-down patternshape, and FIG. 2J is a diagram showing a pattern with a width widerthan a desired pattern;

FIG. 3A is a diagram showing a system configuration in which a CD-SEM, aCS-SEM, an AFM, a CD-SEM mounted in an AFM, an FIB, or an OCD-microscopeis connected to an image-processing/arithmetic processing unit through anetwork, and FIG. 3B is a diagram showing a system configuration havinga plurality of CD-SEMs connected to a network to share a database, animage-processing/arithmetic processing unit, and other systemcomponents, among the plurality of CD-SEMs;

FIG. 4 is a flowchart showing a learning process step and a performanceprocess step to estimate a cross-sectional shape;

FIG. 5 is a flowchart showing a learning process step and a performanceprocess step to estimate process parameters;

FIG. 6 is a flowchart showing a process flow of a method of calculatingcross-sectional shapes and process parameters at the same time;

FIG. 7 is a flowchart showing a process flow of manufacturing processmanagement;

FIG. 8A is a diagram showing a section estimated to acquirecross-sectional shape information on a line pattern, and FIG. 8B is adiagram showing a section estimated to acquire cross-sectional shapeinformation on a hole pattern;

FIG. 9A is a diagram showing an image characteristic quantitycalculation range extracted from a SEM image in order to calculate imagecharacteristic quantities, and FIG. 9B is a diagram showing a lineprofile of the extracted image characteristic quantity calculationrange;

FIG. 10 is a diagram explaining a method of calculating tilt imagecharacteristic quantities indicative of a cross-sectional shape of apattern, from learning data samples or a tilt SEM image to be measured;

FIG. 11A is a cross-sectional view of a pattern of a normalcross-sectional shape, also showing a top-down SEM image and tilt SEMimage associated with the pattern, and FIG. 11B is a cross-sectionalview of a pattern of reduced height, also showing a top-down SEM imageand tilt SEM image associated with the pattern;

FIG. 12A shows, in an upper section, a SEM image of a pattern whose topindicative of a region to be subjected to textural analysis takes arelatively planar shape, and in a lower section a signal strengthfrequency distribution of the textural analysis region, and FIG. 12Bshows, in an upper section, a SEM image of a pattern whose topindicative of a region to be subjected to textural analysis takes a wavyshape, and in a lower section a signal strength frequency distributionof the textural analysis region;

FIG. 13A is a view showing a normal cross-sectional shape of a linepattern; FIG. 13B is a view that shows a line pattern curved inward atits lower end to form a notched cross-sectional shape, FIG. 13C is aview showing a line profile obtained from a SEM image of the normal linepattern of FIG. 13A, the line profile being associated with a right-sidewall of the pattern, and FIG. 13D is a view showing a line profileobtained from a SEM image of the line pattern taking a notchedcross-sectional shape in FIG. 13A, the line profile being associatedwith a right-side wall of the pattern;

FIG. 14A is a cross-sectional view of a pattern having sidewalls of aninverse tapered overhang shape in cross section, FIG. 14B is across-sectional view of a pattern of a normal cross-sectional shape,FIG. 14C shows a line profile calculated from a top-down SEM image ofthe pattern of FIG. 14A that has an inverse tapered overhangcross-sectional shape, FIG. 14D shows a line profile calculated from atilt SEM image obtained by inclining the pattern of FIG. 14A that has aninverse tapered overhang cross-sectional shape, FIG. 14E shows a lineprofile calculated from a top-down SEM image of the pattern having anormal cross-sectional shape, and FIG. 14E shows a line profilecalculated from a tilt SEM image of the pattern having a normalcross-sectional shape;

FIG. 15 illustrates a method of creating a set of learning data forestimating a cross-sectional shape; upper graphs each show adistribution state of a characteristic quantity “mk(t)” which has beencalculated from a CD-SEM image, and lower graphs each show adistribution state of model data “Mk(t)” with which a smoothing processhas been provided;

FIG. 16A graphically shows a relationship between cross-sectional shapeinformation which has been calculated from a SEM image of a patternsubjected to cross-sectional shape estimation, and an imagecharacteristic quantity of the cross-sectional shape, FIG. 16Bgraphically shows a relationship between the cross-sectional shapeinformation and a likelihood function of the image characteristicquantity, and FIG. 16C graphically shows results obtained by multiplyinglikelihood distributions derived from the image characteristic quantity.

FIG. 17 is a diagram showing a method of estimating a cross-sectionalshape, process parameters, or device characteristics of a pattern undermeasurement, using a k-NN method;

FIG. 18 is an explanatory diagram of the k-NN-based method of estimatingthe cross-sectional shape, process parameters, or device characteristicsof the pattern under measurement;

FIG. 19 is an explanatory diagram of an evaluation outline of a learningstate (image characteristic quantities);

FIG. 20A is a diagram explaining a reliability index value (inright-side graph) of sensitivity with respect to changes in thecross-sectional shape or process parameters derived from a distribution(left-side graph) of image characteristic quantities obtained with thechanges in the cross-sectional shape or process parameters, FIG. 20B isa diagram explaining a reliability index value (in right-side graph) ofcontinuity with respect to changes in the cross-sectional shape orprocess parameters derived from a distribution (left-side graph) ofimage characteristic quantities obtained with the changes in thecross-sectional shape or process parameters, FIG. 20C is a diagramexplaining a reliability index value (in right-side graph) of aseparation level with respect to changes in the cross-sectional shape orprocess parameters derived from a distribution (left-side graph) ofimage characteristic quantities obtained with the changes in thecross-sectional shape or process parameters, FIG. 20D is a diagramexplaining a reliability index value (in right-side graph) of learningdensity with respect to changes in the cross-sectional shape or processparameters derived from a distribution (left-side graph) of imagecharacteristic quantities obtained with the changes in thecross-sectional shape or process parameters, and FIG. 20E is a diagramexplaining a reliability index value (in right-side graph) of a modelapplication appropriateness level with respect to changes in thecross-sectional shape or process parameters derived from a distribution(left-side graph) of image characteristic quantities obtained with thechanges in the cross-sectional shape or process parameters;

FIG. 21 is an explanatory diagram of reliability of an estimationengine;

FIG. 22A is a graph showing a relationship between an object to beestimated and a distance to the object, FIG. 22B is a graph of a steeplikelihood distribution with respect to a cross-sectional shape orprocess parameters, and FIG. 22C is a graph of a gentle likelihooddistribution with respect to a cross-sectional shape or processparameters;

FIG. 23 is an explanatory diagram of an estimation engine combinationfor estimating a cross-sectional shape or process parameters of apattern under measurement;

FIG. 24 is a diagram showing an example of a GUI screen menu for thelearning process step; and

FIG. 25 is a diagram showing an example of a GUI screen menu for theperformance process step.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of a system and a method for monitoring semiconductormanufacturing processes according to the present invention, adapted toevaluate and manage a circuit pattern formed on a semiconductor waferduring the semiconductor manufacturing processes, will be describedusing the accompanying drawings. More particularly, the embodimentsrelate to cross-sectional shape and process parameter management of asemiconductor pattern using a CD-SEM apparatus.

A method for estimating a cross-sectional shape of a pattern by using aSEM image to conduct process management with a learning-type engine, asdescribed in U.S. patent application Ser. No. 11/592,175 filed by thepresent inventors, is proposed as an example of the above-outlinedmethod for managing a cross-sectional shape of a semiconductor pattern.In the proposed method, a cross-sectional shape of a pattern to bemeasured, or process parameters of the pattern are calculated byutilizing image characteristic quantities effective for estimatingcross-sectional shape or process parameters of the pattern, based on aSEM image of the pattern, then saving a relationship between the imagecharacteristic quantities and the cross-sectional shape or processparameters of the pattern beforehand in a database (the relationship ishereinafter called learning data), and collating image characteristicquantity data calculations from the SEM image of the pattern with thelearning data.

Accordingly, the present invention is adapted to realize the followingwhen learning data is created from measurement results on variouspatterns each previously formed into a specific cross-sectional shape orusing specific process parameters. That is to say, the number oflearning data samples and/or a distribution state thereof is such thatduring cross-sectional shape estimating or process parameter estimating,sufficient estimation accuracy can be obtained even in estimatedfluctuation ranges of various parameters used for the estimating process(i.e., even in a fluctuation range of a cross-sectional shape likely tobe formed because of changes in process parameters, or fluctuationranges of process parameters likely to become effective values duringthe formation of the pattern).

The present invention is also adapted such that if, duringcross-sectional shape estimating or process parameter estimating, thenumber of learning data samples and/or the distribution state thereof isjudged to be inappropriate for obtaining sufficient estimation accuracyeven in the estimated fluctuation ranges of the estimating parametersused, useful information will be supplied for a user to identify thepattern of a cross-sectional shape or process parameters to be subjectedto additional learning.

In addition, in the present invention, when the image characteristicquantities that have been calculated from the SEM image of thesemiconductor pattern are used to monitor the cross-sectional shape orthe process parameters, the above-mentioned estimation accuracy isimproved by selection of the image characteristic quantities and/oradjustment of weight between the image characteristic quantities. Inthat case, a method is provided so that while setting judgment criteriafor the above selection and/or adjusting the weight, the user can judgewhether the number of learning data samples and/or the distributionstate thereof is such that sufficient estimation accuracy can beobtained even in the estimated fluctuation ranges of the estimatingparameters used.

Furthermore, in the present invention, during selection of the optimalengine used for estimating the cross-sectional shape or the processparameters, the user can easily select the estimation engine whilechecking the distribution state of the learning data and theabove-mentioned estimating performance against the judgment criteria forthe selection.

Furthermore, in the present invention, in order to collect the learningdata, the patterns formed into various cross-sectional shapes or usingvarious process parameters are estimated. For estimation ofcross-sectional shapes and process parameters, an appropriate amount oflearning data and/or acquiring appropriate distribution information onthe samples may not be easily acquired in order to obtain sufficientestimation accuracy even in the estimated fluctuation ranges of theestimating parameters used, in terms of semiconductor-manufacturingapparatus adjustment or creation time or the like. Even if the amount oflearning data actually acquired is not sufficient, estimating results onthe cross-sectional shapes or on the process parameters can beappropriately analyzed and evaluated in quantitative form by, forexample, presenting reliability data via a GUI function.

(Example of a CD-SEM Apparatus)

FIG. 1A is a schematic block diagram showing a configuration of ascanning electron microscope (SEM) which acquires a secondary electron(SE) image or backscattered electron (BSE) image of a sample(semiconductor wafer) in the present invention. Hereinafter, the SEimage and the BSE image are collectively called a SEM image. Also, theimage acquired in this example includes part or all of a top-down imageor tilt image of a circuit pattern shape to be measured, the top-downimage or tilt image being obtained during observation of the circuitpattern shape from a perpendicular direction or an arbitrary tilt angledirection, respectively.

The scanning electron microscope (CD-SEM) 401 (420, 421) has an electronoptical system 102 that includes: an electron gun 103 for emitting anelectron beam (primary electrons) 104; a condenser lens 105 forconverging the electron beam 104 emitted from the electron gun 103; adeflector 106 controlled by a deflection controller 120 and deflectingthe converged electron beam 104; an objective lens 108 controlled by thedeflection controller 120 and focusing on a semiconductor wafer 101 theelectron beam deflected by the deflector 106 before being irradiated; anExB deflector 107 for directing secondary electrons originated from thesemiconductor wafer 101, to a secondary electron detector 109; thesecondary electron detector 109 for detecting the secondary electronsoriginated from the semiconductor wafer 101; and backscattered electrondetectors 110, 110 for directing backscattered electrons originated fromthe semiconductor wafer 101.

The scanning electron microscope (CD-SEM) 401 (420, 421) also has an XYstage 117 on which to rest the semiconductor wafer 101. The scanningelectron microscope (CD-SEM) 401 (420, 421) further has a stage tiltfunction to conduct stage control by a stage controller 119. The XYstage 117 moves the semiconductor wafer 101, thus enabling an arbitraryportion of the wafer 101 to be imaged. Hereinafter, changing anobservation position using the XY stage 117 is called “stage shift” andchanging the observation position by deflecting the electron beam usingthe deflector 106 is called “beam shift.”

In this way, the deflector 106 and the objective lens 108 control anirradiation position and diameter reduction (converging) of the electronbeam 104 so that any position on the semiconductor wafer 101, the sampleon the stage 117, is irradiated with the focused electron beam.Secondary electrons and backscattered electrons are emitted from thesemiconductor wafer 101 that has been irradiated with the electron beam,and the secondary electrons are detected by the secondary electrondetector 109. The backscattered electrons are detected by thebackscattered electron detectors 110 and 111. The backscattered electrondetectors 110 and 111 are installed in directions different from eachother. The secondary electrons and backscattered electrons that havebeen detected by the secondary electron detector 109 and thebackscattered electron detectors 110 and 111, respectively, areconverted into digital signal form by A/D converters 112, 113, 114, thenstored into an image memory 122 of a processor/controller 115, andsubjected to appropriate image processing by a CPU 121 according toparticular needs. Although two backscattered-electron image detectors,110 and 112, are shown in the example of FIG. 1A, the number ofbackscattered-electron image detectors can be reduced or increased.

FIGS. 1B and 1C show a method in which, when the semiconductor wafer isscanned with electron beams for irradiation, signal quantities of theelectrons emitted from the semiconductor wafer are converted intoimages. For example, as shown in FIG. 1B, the semiconductor wafer isscanned and irradiated with electron beams 131-133 or 134-136 in an x-or y-direction, respectively. The scanning direction can be varied bychanging a deflecting direction of the electron beams. Positions on thesemiconductor wafer where it has been scanned and irradiated with theelectron beams 131 to 133 in the x-direction are denoted as referencenumbers G1 to G3, respectively. Similarly, positions on thesemiconductor wafer where it has been scanned and irradiated with theelectron beams 134 to 136 in the x-direction are denoted as referencenumbers G4 to G6, respectively. The signal quantities of the electronswhich have been emitted from the positions G1-G3 become brightnessvalues formed by pixels H1 to H6, respectively, within an image 139which is shown in FIG. 1C (the subscripts 1 to 6 at the lower right ofsymbol G are respectively associated with those of symbol H). Referencenumber 138 denotes a coordinate system indicating the x- andy-directions in the image.

Several methods are available to obtain a tilt SEM image of the circuitpattern shape when observed from an arbitrary tilt angle direction usingthe CD-SEM 401 (420, 421) shown in FIG. 1A. Examples of these methodsare: (1) a scheme of acquiring a tilt image by deflecting the electronbeams irradiated from the electron optical system, and thus giving atilt angle to the irradiation of the electron beams (this scheme isdescribed in, for example, Japanese Patent Laid-Open No. 2000-348658),(2) an imaging scheme by inclining the stage 117 itself that moves thesemiconductor wafer (in FIG. 1A, the stage is inclined at an angle 218),and (3) an imaging scheme by mechanically inclining the electron opticalsystem itself.

The processor/controller 115 shown in FIG. 1A is a computer system,which sends control signals to the stage controller 119 and thedeflection controller 120 and performs various processing and controlfunctions such as processing the observation image on the semiconductorwafer 101. The processor/controller 115 is connected to a display 116and has a GUI (Graphic User Interface) function that display images andothers to a user.

Part or all of the processing and control functions performed by theprocessor/controller 115 can also be allocated to a plurality ofdifferent processing terminals. In addition, the processor/controller115 is connected to a network 400 as shown in FIG. 3A or 3B, and isconstructed to intercommunicate with other apparatus constituentelements 402-406, 420, 421, with an image-processing/arithmeticprocessing unit 407 that performs the processes shown in FIG. 4, such asa learning process 300 and a performance evaluation process 350, andwith a database 408.

(Examples of Semiconductor Pattern Cross-Sectional Shapes)

Typical examples of semiconductor pattern cross-sectional shapes whichare subjected to estimating in the present invention are described belowusing FIGS. 2A to 2J. A normal cross-sectional shape of a semiconductorpattern, and abnormal cross-sectional shapes of semiconductor patternsare shown by way of example in FIGS. 2A-2J. Cross-sectional shape 200shown in FIG. 2A is an example of the cross-sectional shape typicallyconsidered to be one of the most desirable shapes achievable insemiconductor patterns. In this example, sidewalls of the pattern areessentially perpendicular in tilt angle θ. In addition, at patternbottom 221, the sidewalls of the pattern are essentially orthogonal tothe surface of an underlayer, and at pattern top 220, a top layer of thepattern and the sidewalls thereof are essentially orthogonal to eachother.

In contrast to FIG. 2A, FIGS. 2B to 2J show cross-sectional shapes 201to 213 that are generally classified as abnormal semiconductor patternshapes, and these are examples of a pattern in which desired devicecharacteristics cannot be obtained. The pattern shapes 201-213, however,may be intentionally formed to obtain desired circuit composition, asshown in FIGS. 2B-2J.

Next, each shape is briefly described below. The cross-sectional shape201 shown in FIG. 2B is a pattern shape with pattern sidewalls inclinedat angle θ smaller than 90°, and this pattern shape may be called aforward tapered shape. The cross-sectional shape 202 shown in FIG. 2C isa pattern shape with pattern sidewalls inclined at angle θ greater than90°, and this pattern shape may be called an inverse tapered shape. Thecross-sectional shape 203 shown in FIG. 2D is a pattern shape with athin pattern central portion and inward curved sidewalls 222, and thispattern shape may be called a bowing shape. The cross-sectional shape204 shown in FIG. 2E is a pattern shape with round upper corners 223 ofthe pattern. The cross-sectional shape 205 shown in FIG. 2F is a patternshape with protuberant upper corners 223 of the pattern, and thispattern shape may be called an overhung shape. The cross-sectional shape206 shown in FIG. 2G is a pattern shape with skirt-like portions 225 atthe bottom of the pattern, and this pattern shape may be called a skirtshape. The cross-sectional shape 207 shown in FIG. 2H is a pattern shapewith underlayer-sidewall crossover portions 226 disposed more internallythan upper sidewall portions of the pattern, and this pattern shape maybe called a notched shape. The patterns 208, 209, 210, 211 shown in FIG.2I each have a shape smaller than a desired vertical size, and each ofthese pattern shapes may be called a thinned-down shape. The pattern 212shown in FIG. 2J is smaller than a desired horizontal size, and thepattern 213 shown in FIG. 2J is greater than a desired horizontal size.

The cross-sectional shapes 202-213 shown in FIGS. 2B-2J are examples ofabnormal shapes caused by the inappropriate process parameters usedduring semiconductor manufacturing. For semiconductor circuit patterns,gate length becomes a dimension of the pattern bottom and thus itbecomes important to measure the dimension of the bottom independentlyof the pattern shape, but during a gate-forming process, a source/drainof a transistor is formed by ion implantation through a wiring pattern.Accordingly, tilt angles of the pattern sidewalls and the shape of thepattern bottom affect treatment results on the ion implantation process,thus leading to changes in device characteristics. It is thereforeimportant to manage the above-mentioned cross-sectional shape of thegate pattern properly. Also, during an exposure process, a pattern isthermally transferred to the surface of a resist according to exposuremask and then a developing operation based on the transferred pattern isconducted to form the resist pattern.

Next, an etching process is conducted to etch an underlayer using theformed resist pattern as a mask pattern. During the etching process, ifthe resist pattern has an abnormality in its cross-sectional shape,formation of an etching pattern on the underlayer is also likely tobecome abnormal during the etching. Hence, it is very important toevaluate the cross-sectional shape of the pattern during both thegate-forming process and the exposure process. A method of calculatingthe cross-sectional shape will be described later herein. The presentinvention is characterized in that it monitors the cross-sectionalshape.

(Example of Process Parameters)

Next, a typical example of the process parameters estimated according tothe present invention is described below. In the present invention, thekinds of process parameters described below include a position of focusin an exposure machine, a dose rate, an exposure time, a bakingtemperature, a baking time, an etching time in an etching apparatus, aninternal temperature of a chamber, a gas flow rate, or a gas pressure.Also, the present invention calculates part or all of these parameters.Although the above process parameters have been enumerated as an exampleof the process parameters estimated, the present invention is notlimited to the above process parameters and the invention ischaracterized in that it monitors the process parameters which requireadjustment during an exposure process or an etching process.

(Examples of a Semiconductor Process-Estimating System)

Next, configurations of a semiconductor process-estimating system forevaluating and managing semiconductor wafer circuit patterns accordingto the present invention during semiconductor-manufacturing processes,and more particularly, system configurations for managing across-sectional shape and process parameters of a semiconductor patternusing a CD-SEM(s) are described below using FIGS. 3A, 3B. An embodimentof the system configuration shown in FIG. 3A is first described below.In this system configuration, part or all of the system constituentelements 401-408 described below are connected via a network 400 and canshare the input information and output information used forcross-sectional shape or process parameter estimating or for calculationof various reliability data. Connected to the network 400 are: a CD-SEM401; part or all of the group consisting of a cross-sectional SEM(CS-SEM) 402, an AFM (Atomic Force Microscope) 403, an AMF-mountedCD-SEM 404, an FIB (Focused Ion Beam) microscope 405, and an OCD(Optical Critical Dimension) microscope 406; animage-processing/arithmetic processing unit 407 inclusive of a learningprocessor 4071 and of a performance processor 4072 and with a connecteddisplay 409 having a GUI function; and a database 408. The CD-SEM 401 isused to acquire SEM images of pattern shapes to be measured.

The CS-SEM) 402, the AFM 403, the AMF-mounted CD-SEM 404, the FIBmicroscope 405, or the OCD microscope 406 are used to measurecross-sectional geometric data to be defined as correctly estimated datain the learning process steps (300) described later. Theimage-processing/arithmetic processing unit 407 undertakes imageprocessing for calculation of image characteristic quantities from eachSEM image, cross-sectional shape estimating or process parameterestimating, and arithmetic processing such as reliability datacalculation. The database 408 is used to save the data used forcross-sectional shape estimation or process parameter estimation of thepattern shape to be measured, and for the reliability data calculationconducted together with the estimating process mentioned above. Thekinds of data saved include the SEM image, cross-sectional shapeestimation results, process parameters, image-processing parameters,cross-sectional shape estimation process parameters, process estimatingparameters, and other information.

FIG. 3B is a diagram showing another embodiment of a systemconfiguration in which a plurality of CD-SEMs, 401, 420, 421, areconnected to a network 400 to share a database 408, animage-processing/arithmetic processing unit 407, and other elements. Inthis system configuration with the CD-SEMs 420 and 421 connected to thesystem configuration of FIG. 3A via the network 400, the same learningdata as used during cross-sectional shape or process parameterestimation can be used (the learning data is a combination of SEM imagesand cross-sectional shape information or process parameter informationassociated with the SEM images). Constructing the system in this waymakes it possible to efficiently estimate a cross-sectional shape andprocess parameters.

On the basis of the SEM images and cross-sectional shape information orprocess parameters acquired as learning data from the CD-SEM 401 andother system components, the learning processor 4071 within theimage-processing/arithmetic processing unit 407 executes the learningprocess steps (300) and (500) shown in FIGS. 4 and 5, respectively.After that, on the basis of an estimation engine that the learningprocessor 4072 has determined along with the above learning data, andthe SEM images acquired by the CD-SEM 401 or the like, the performanceprocessor 4072 within the image-processing/arithmetic processing unit407 executes the performance process steps (350) and (550) shown inFIGS. 4 and 5, respectively, and thus evaluates the cross-sectionalshape or the process parameters. Instead of the performance processor4072, an internal CPU 121 of a processor/controller 115 provided in theCD-SEM 401 (420, 421) may execute the performance process steps (350,550).

(Example of Cross-Sectional Shape Estimating)

Next, a process flow of the semiconductor pattern cross-sectional shapeestimating process and reliability calculation on cross-sectional shapeestimation results, executed by, for example, the learning processor4071 and performance processor 4072, respectively, in the presentinvention, is described below using FIG. 4. The estimation process isbroadly divided into learning process steps (300) and performanceprocess steps (350).

The learning process steps (300) are first described below. The learningprocess steps (300) consist of a learning data acquisition step (301),an image characteristic quantity selection and/or adjustment step (323),and an estimation engine selection and/or adjustment step (319).Execution of the latter two steps, 323 and 319, is based on thereliability described later herein. Acquisition of SEM images in step302 from the semiconductor patterns of various shapes that have beencreated using the method described later (these created patterns arehereinafter called the learning samples), and acquisition of associatedcross-sectional shape information in step 303 are conducted in thelearning data acquisition step (301). The acquisition of thecross-sectional shape information in step 303 is conducted using AFM(Atomic Force Microscope) measurement, OCD (Optical Critical Dimension)measurement, cross-sectional SEM (CS-SEM) measurement, or othercross-sectional shape measuring instruments 401-406, 420, 421. Thus,cross-sectional shapes of the learning samples are measured.

Data that consists of a combination between the above-obtained SEMimages and associated cross-sectional shape information of the learningsamples is called learning data. In step 304, the learning data that wasacquired in step 301 by the CD-SEM 401 (420, 421) and other measuringinstruments 402-406 is registered in the database 408 via the network400, for example. In step 305, the learning processor 4071 calculatesthe later-described image characteristic quantities from the acquiredSEM images, and then back in step 304, registers the imagecharacteristic quantities, together with the learning data, in thedatabase 408. The image characteristic quantities, although detailedlater herein, have a correlation with changes in three-dimensionalshapes of the semiconductor patterns.

In step 306, the learning processor 4071 learns the later-describedestimation engine by using the learning data that has been saved in thedatabase 408 (i.e., the data consisting of a combination between the SEMimages and associated cross-sectional shape information). The learningprocessor 4071 next executes step 307 to calculate reliability using theestimation engine that the learning processor has learned. Inreliability calculation step 307, three kinds of reliability data arecalculated. That is to say, reliability of an image characteristicquantity distribution is calculated in step 308, reliability of theestimation engine is calculated in step 309, and reliability of theestimation results is calculated in step 310. The three kinds ofreliability data become index values for judging whether the number oflearning data samples and/or the distribution thereof is appropriate forobtaining sufficient estimation accuracy in estimated fluctuation rangesof the cross-sectional shapes estimated using the estimation engine. Theuser can set the estimated fluctuation ranges by manually entering eachrange using the later-described GUI (Graphic User Interface) of thedisplay 409 or 116 or the like, or by adopting default settings or thelater-described data saved in the database.

Also, the reliability data is presented to the user via the GUI in step313 to enable the user to understand settings of the learning data or astate of the estimation engine and to select and/or adjust theestimation engine (steps 323, 329) while confirming the reliabilitydata. In the present invention, since, in this way, the three kinds ofreliability data calculated in step 307 (i.e., the reliability of theimage characteristic quantity distribution, calculated in step 308, thereliability of the estimation engine, calculated in step 309, and thereliability of the estimation results, calculated in step 310) arepresented to the user via the GUI, the user can not only use thereliability data as the index data for judging whether the number oflearning data samples and/or the distribution thereof is appropriate forobtaining sufficient estimation accuracy in the estimated fluctuationranges of the cross-sectional shapes estimated using the estimationengine, but also understand the settings of the learning data or thestate of the estimation engine and select and/or adjust the estimationengine while confirming the reliability data.

As will be detailed later herein, on the basis of the reliability dataof the image characteristic quantity distribution that was obtained instep 308, the learning processor 4071 evaluates the learning state instep 311 and judges in step 314 whether the image characteristicquantities are appropriate for estimating the cross-sectional shape ofthe pattern. If it is found in step 320 that the image characteristicquantities are not appropriate, the learning processor 4071 executesstep 321 to judge whether additional learning is necessary. If it isfound in step 343 that additional learning is necessary, the learningprocessor 4071 returns to step 301 to re-acquire learning data (anothercombination between SEM images and associated cross-sectional shapeinformation) from the learning samples or to add learning samples andacquire new learning data. After the judgment in step 321, if it isfound in step 344 that additional learning is unnecessary, the learningprocessor 4071 executes step 322, as will be detailed later, to judgewhether the characteristic quantities require adjustment. If thejudgment results that were obtained in step 322 indicate that theadjustment of the characteristic quantities is necessary, the learningprocessor 4071 conducts image characteristic quantity selections and/orweight adjustments thereof in step 323 and then returns to step 306 tore-learn the estimation engine by using adjusted characteristicquantities. After this, the learning processor 4071 executes step 315 toevaluate the estimation engine on the basis of the reliability thereofthat was calculated in step 309.

Next, on the basis of evaluation results on the estimation engine, thelearning processor 4071 judges in step 316, during cross-sectional shapeestimation, whether the estimation engine can obtain sufficientestimation accuracy in the estimated fluctuation range of thecross-sectional shape estimated. If it is found in step 318 that theestimation engine does not suffice, the learning processor 4071 executesstep 319, as will be detailed later, to change the estimation engineand/or adjust the weight between engines, and then executes step 306 tolearn another estimation engine obtained after the change or the weightadjustment.

Next, after executing step 310 to calculate reliability of the newestimation results obtained, the learning processor 4071 evaluates thenew estimation results in step 312. After evaluating the new estimationresults, the learning processor 4071 executes step 324 to conduct anacceptability judgment on the new estimation results, based onevaluation results. If it is found in step 325 that the new estimationresults are not reliable enough, the learning processor 4071 executesstep 321 to judge whether additional learning is necessary. If it isfound in step 343 that additional learning is necessary, the learningprocessor 4071 returns to step 301 to re-acquire learning data from thelearning samples or to add learning samples and acquire new learningdata. After the judgment in step 321, if it is found in step 344 thatadditional learning is unnecessary, the learning processor 4071 executesstep 322, as will be detailed later, to judge whether the characteristicquantities require adjustment. If the judgment results that wereobtained in step 322 indicate that the adjustment of the characteristicquantities is necessary, the learning processor 4071 conducts imagecharacteristic quantity selections and/or weight adjustments thereof instep 323 and then returns to step 306 to re-learn the estimation engineby using adjusted characteristic quantities.

When the image characteristic quantity appropriateness judgment in step314, the estimation result acceptability judgment in step 324, and theestimation engine reliability judgment in step 316 indicate that thecross-sectional shape estimation accuracy obtained duringcross-sectional shape estimating based on the estimation engine and onthe learning data is high enough for obtaining sufficient estimationaccuracy in the estimated fluctuation range of the cross-sectional shapeestimated, if it is judged during ANDing operations (step 327) betweenall the above appropriateness/acceptability judgment results (in steps314, 324, 316) that necessary conditions are satisfied, the learningprocessor 4071 determines the learning data and the estimation engine aslearning data and estimation engine 331 to be used in the performanceprocess steps (350) described next, and becomes ready for supplying(transmitting) the learning data and estimation engine 331 to theperformance processor 4072 or the like.

Next, the performance process step (350) is described below. In theestimation steps (332, 333), the performance processor 4072 or the likecalculates a cross-sectional shape of a pattern to be measured, andreliability of cross-sectional shape estimation results, by using theestimation engine and learning data (data consisting of a combinationbetween SEM images and associated cross-sectional shape information)determined in the learning process steps (300). First, step 329 isexecuted to acquire a SEM image of the pattern from the CD-SEM 401 (420,421) and then store the SEM image into the database 408, for example.The performance processor 4072 or the like calculates imagecharacteristic quantities from the acquired SEM image in step 330. Theimage characteristic quantities calculated here are of the same kind asthat of the image characteristic quantity data that was calculated fromthe SEM image in step 305 of the learning process steps (300). As willbe detailed later, the performance processor 4072 or the like executesstep 332 to monitor the cross-sectional shape of the pattern, and step333 to calculate the reliability of the estimation results, from theimage characteristic quantities that were calculated in step 330, andfrom the estimation engine and learning data 331 that were determined instep 328. Next, whether the reliability of the estimation resultssatisfies the threshold level required is judged in step 334 and if thereliability is judged to satisfy the threshold level, the estimatedcross-sectional shape is output in step 337 as the cross-sectional shapeof the pattern.

In step 339, the image-processing/arithmetic processing unit 407evaluates the cross-sectional shape that has been output from theperformance processor 4072, for example, and examines whether thecross-sectional shape is a desired one. If, in step 341, the patternshape is found to satisfy design standards, an associated signal istransmitted from the image-processing/arithmetic processing unit 407 viathe network 400 to a process management apparatus (not shown) that ismanaging the semiconductor-manufacturing line, and the pattern is sentto next process site. If, in step 340, the pattern shape is found not tosatisfy the design standards, the image-processing/arithmetic processingunit 407 outputs a control signal to a process apparatus (e.g., theexposure machine 702 or etching apparatus 704 shown in FIG. 7) via thenetwork 400 to indicate that the pattern needs to be fed back to anassociated process site, and the image-processing/arithmetic processingunit 407 feeds back the pattern to the associated process site in step342. As a result, process parameters (exposure parameters or etchingparameters) are adjusted in the process apparatus (e.g., the exposuremachine 702 or the etching apparatus 704) and then a pattern satisfyingthe design standards is formed. When the estimated cross-sectional shapeis output from the performance processor 4072, it can also be output to,for example, a GUI screen of the display 409 for presentation to theuser, in step 345. In addition, although it has been described that theevaluation of the cross-sectional shape in step 339 is conducted in theimage-processing/arithmetic processing unit 407, this evaluation stepmay be executed in the process apparatus (e.g., the exposure machine 702or the etching apparatus 704) and if the design standards are notsatisfied in step 340, the process parameters (exposure parameters oretching parameters) may be adjusted in the process apparatus mentionedabove. Furthermore, in step 345, the estimated cross-sectional shape canbe presented to a display (not shown) that is connected to each processdevice.

If the acceptability judgment of the reliability of the estimationresults in step 330 of the performance process steps (350) indicatesthat the cross-sectional shape estimation results are found to beinsufficient, the learning processor 4071 executes step 321 in thelearning process steps (300) to judge whether additional learning isnecessary for re-learning. If it is found in step 343 that additionallearning is necessary, the learning processor 4071 returns to step 301to re-acquire learning data from the learning samples or to add learningsamples and acquire new learning data. After the judgment in step 321,if it is found in step 344 that additional learning is unnecessary, thelearning processor 4071 executes step 322, as will be detailed later, tojudge whether the image characteristic quantities require adjustment. Ifthe adjustment of the image characteristic quantities is necessary, thelearning processor 4071 conducts image characteristic quantityselections and/or weight adjustments thereof in step 323 and thenreturns to step 306 to re-learn the estimation engine by using adjustedimage characteristic quantities.

The present invention is characterized particularly in that part or allof the various reliability data calculated in steps 308, 309, 310 duringthe execution of the reliability calculation step (307) within thelearning process steps (300) is presented from, for example, the GUI ofthe display 409 to the user in step 313.

The present invention is characterized in that the reliability of thepattern cross-sectional shape estimation results that was calculated inthe estimation result reliability calculation step (333) of theperformance process steps (350) is also presented from, for example, theGUI of the display 409 to the user in step 338. Since the reliability ofthe pattern cross-sectional shape estimation results that was thuscalculated in step 333 is presented to the user, it becomes possible forthe user to perform more appropriate judgments on the estimationresults.

Using various reliability data in the learning process steps (300) ofthe semiconductor pattern cross-sectional shape estimating technique ofthe learning type in accordance with the process flow described abovemakes it possible to judge, during estimating of a cross-sectionalshape, whether sufficient learning data has been acquired for obtainingsufficient estimation accuracy in the estimated fluctuation range of thecross-sectional shape estimated.

In the performance process steps (350), the reliability of the patternshape estimation results that was obtained in step 338 can also becalculated, and the user can perform more appropriate judgments on theestimation results, based on the calculated reliability.

(Example of Process Parameter Estimating)

Next, a process flow of the semiconductor pattern process parameterestimation process and reliability calculation on process parameterestimation results, executed by, for example, the learning processor4071 and performance processor 4072, respectively, in the presentinvention, is described below using FIG. 5. The estimation process isbroadly divided into learning process steps (500) and performanceprocess steps (550).

The learning process steps (500) are first described below. The learningprocess steps (500) consist of a learning data acquisition step (501),an image characteristic quantity selection and/or adjustment step (523),and an estimation engine selection and/or adjustment step (519).Execution of the latter two steps, 523 and 519, is based on thereliability described later herein. Acquisition of SEM images in step502 and acquisition of associated cross-sectional shape information instep 503 are conducted in the learning data acquisition step (501). Instep 502, SEM images are acquired from semiconductor patterns that havebeen created using the later-described method and formed using processparameters assigned to a process apparatus, for example, the exposuremachine 702 or etching apparatus 704 shown in FIG. 7 (thesesemiconductor patterns are hereinafter called learning samples).Cross-sectional shape information associated with the SEM images isacquired in step 503. In order to acquire the cross-sectional shapeinformation in step 503, patterns on FEM (Focus Exposure Matrix) wafersare measured using various exposure parameters assigned to the exposuremachine 702, for example, and a combination of the SEM images andprocess parameters acquired during the measurements is obtained as alearning sample.

Data that consists of the combination between the above-obtained SEMimages and associated cross-sectional shape information is calledlearning data. In step 504, the learning data that was acquired in step501 by the CD-SEM 401 (420, 421) is registered in the database 408 viathe network 400, for example. In step 505, the learning processor 4071calculates the later-described image characteristic quantities from theacquired SEM images, and then back in step 504, registers the imagecharacteristic quantities, together with the learning data, in thedatabase 408. The image characteristic quantities, although detailedlater herein, have a correlation with changes in three-dimensionalshapes of the semiconductor patterns. In step 506, the learningprocessor 4071 learns the later-described estimation engine by using thelearning data that has been saved in the database 408.

Next, the learning processor 4071 executes step 507 to calculatereliability using the estimation engine that the learning processor haslearnt. In reliability calculation step 507, three kinds of reliabilitydata are calculated. That is to say, reliability of an imagecharacteristic quantity distribution is calculated in step 508,reliability of the estimation engine is calculated in step 509, andreliability of the estimation results is calculated in step 510. Thethree kinds of reliability data become index values for judging whetherthe number of learning data samples and/or the distribution thereof isappropriate for obtaining sufficient estimation accuracy in estimatedfluctuation ranges of the cross-sectional shapes estimated using theestimation engine. The user can set the estimated fluctuation ranges bymanually entering each range using the later-described GUI (Graphic UserInterface) of the display 409 or 116 or the like, or by adopting defaultsettings or the later-described data saved in the database.

Also, the reliability data is presented to the user via the GUI in step513 to enable the user to understand settings of the learning data or astate of the estimation engine and to select and/or adjust theestimation engine (steps 523, 519) while confirming the reliabilitydata. In the present invention, since, in this way, the three kinds ofreliability data calculated in step 507 (i.e., the reliability of theimage characteristic quantity distribution, calculated in step 508, thereliability of the estimation engine, calculated in step 509, and thereliability of the estimation results, calculated in step 510) arepresented to the user via the GUI, the user can not only use thereliability data as the index data for judging whether the number oflearning data samples and/or the distribution thereof is appropriate forobtaining sufficient estimation accuracy in the estimated fluctuationranges of the cross-sectional shapes estimated using the estimationengine, but also understand the settings of the learning data or thestate of the estimation engine and select and/or adjust the estimationengine while confirming the reliability data.

As will be detailed later herein, on the basis of the reliability dataof the image characteristic quantity distribution that was obtained instep 508, the learning processor 4071 evaluates the learning state instep 511 and judges in step 514 whether the image characteristicquantities are appropriate for estimating the cross-sectional shape ofthe pattern. If it is found in step 520 that the image characteristicquantities are not appropriate, the learning processor 4071 executesstep 521 to judge whether additional learning is necessary. If it isfound in step 543 that additional learning is necessary, the learningprocessor 4071 returns to step 501 to re-acquire learning data (anothercombination between SEM images and associated cross-sectional shapeinformation) from the learning samples or to add learning samples andacquire new learning data. After the judgment in step 521, if it isfound in step 544 that additional learning is unnecessary, the learningprocessor 4071 executes step 522, as will be detailed later, to judgewhether the image characteristic quantities require adjustment. If thejudgment results that were obtained in step 522 indicate that theadjustment of the image characteristic quantities is necessary, thelearning processor 4071 conducts image characteristic quantityselections and/or weight adjustments thereof in step 523 and thenreturns to step 506 to re-learn the estimation engine by using adjustedimage characteristic quantities.

After this, the learning processor 4071 executes step 515 to evaluatethe estimation engine on the basis of the reliability thereof that wascalculated in step 509. Next, on the basis of evaluation results on theestimation engine, the learning processor 4071 judges in step 516,during cross-sectional shape estimation, whether the estimation enginecan obtain sufficient estimation accuracy in the estimated fluctuationrange of the cross-sectional shape estimated. If it is found in step 518that the estimation engine does not suffice, the learning processor 4071executes step 519, as will be detailed later, to change the estimationengine and/or adjust the weight between engines, and then executes step506 to learn another estimation engine obtained after the change or theweight adjustment. Next after executing step 510 to calculatereliability of the new estimation results obtained, the learningprocessor 4071 evaluates the new estimation results in step 512. Afterevaluating the new estimation results, the learning processor 4071executes step 524 to conduct an acceptability judgment on the newestimation results, based on evaluation results. If it is found in step525 that the new estimation results are not reliable enough, thelearning processor 4071 executes step 521 to judge whether additionallearning is necessary. If it is found in step 543 that additionallearning is necessary, the learning processor 4071 returns to step 501to re-acquire learning data from the learning samples or to add learningsamples and acquire new learning data.

After the judgment in step 521, if it is found in step 544 thatadditional learning is unnecessary, the learning processor 4071 executesstep 522, as will be detailed later, to judge whether the imagecharacteristic quantities require adjustment. If the judgment resultsthat were obtained in step 522 indicate that the adjustment of the imagecharacteristic quantities is necessary, the learning processor 4071conducts image characteristic quantity selections and/or weightadjustments thereof in step 523 and then returns to step 306 to re-learnthe estimation engine by using adjusted image characteristic quantities.

When the image characteristic quantity appropriateness judgment in step514, the estimation result acceptability judgment in step 524, and theestimation engine reliability judgment in step 516 indicate that thecross-sectional shape estimation accuracy obtained duringcross-sectional shape estimating based on the estimation engine and onthe learning data is high enough for obtaining sufficient estimationaccuracy in the estimated fluctuation range of the cross-sectional shapeestimated, if it is judged during ANDing operations (step 527) betweenall the above appropriateness/acceptability judgment results (in steps514, 524, 516) that necessary conditions are satisfied, the learningprocessor 4071 determines the learning data and the estimation engine aslearning data and estimation engine 531 to be used in the performanceprocess steps (550) described next, and becomes ready for supplying(transmitting) the learning data and estimation engine 531 to theperformance processor 4072 or the like.

Next, the performance process step (550) is described below. In theestimating steps (532, 533), the performance processor 4072 calculatesprocess parameters for a pattern to be measured, and reliability ofprocess parameters estimation results, by using the estimation engineand learning data that were determined in the learning process steps(500). First, step 529 is executed to acquire a SEM image of the patternfrom the CD-SEM 401 (420, 421) and then store the SEM image into thedatabase 408, for example. The performance processor 4072 or the likecalculates image characteristic quantities from the acquired SEM imagein step 530. The image characteristic quantities calculated here are ofthe same kind as that of the image characteristic quantity data that wascalculated from the SEM image in step 505 of the learning process steps(500). As will be detailed later, the performance processor 4072 or thelike executes step 532 to estimate process parameters for a pattern tobe measured, and step 533 to calculate the reliability of the estimationresults, from the image characteristic quantities that were calculatedin step 530, and from the estimation engine and learning data 531 thatwere determined in step 528. Next, whether the reliability of theestimation results satisfies the threshold level required is judged instep 534 and if the reliability is judged to satisfy the thresholdlevel, the estimated process parameters are output in step 537 as theprocess parameters of the pattern to be measured.

In step 539, the image-processing/arithmetic processing unit 407evaluates the process parameters that has been output from theperformance processor 4072, for example, and examines whether thecross-sectional shape is a desired one. If, in step 541, the patternshape is found to satisfy design standards, an associated signal istransmitted from the image-processing/arithmetic processing unit 407 viathe network 400 to a process management apparatus (not shown) that ismanaging the semiconductor-manufacturing line, and the pattern is sentto next process site. If, in step 540, the pattern shape is found not tosatisfy the design standards, the image-processing/arithmetic processingunit 407 outputs a control signal to the process apparatus (e.g., theexposure machine 702 or etching apparatus 704 shown in FIG. 7) via thenetwork 400 to indicate that the pattern needs to be fed back to anassociated process site, and the image-processing/arithmetic processingunit 407 feeds back the pattern to the associated process site in step542. As a result, process parameters (exposure parameters or etchingparameters) are adjusted in the process apparatus (e.g., the exposuremachine 702 or the etching apparatus 704) and then a pattern satisfyingthe design standards is formed. When the estimated cross-sectional shapeis output from the performance processor 4072, it can also be output to,for example, a GUI screen of the display 409 for presentation to theuser, in step 545. In addition, although it has been described that theevaluation of the process parameters in step 539 is conducted in theimage-processing/arithmetic processing unit 407, this evaluation stepmay be executed in the process apparatus (e.g., the exposure machine 702or the etching apparatus 704) and if the design standards are notsatisfied in step 540, the process parameters (exposure parameters oretching parameters) may be adjusted in the process apparatus mentionedabove. Furthermore, in step 545, the estimated process parameters can bepresented to a display (not shown) that is connected to each processdevice.

If the acceptability judgment of the reliability of the estimationresults in step 534 of the performance process step (550) indicates thatthe process parameters estimation results are found to be insufficient,the learning processor 4071 executes step 521 in the learning processstep (500) to judge whether additional learning is necessary forre-learning. If it is found in step 543 that additional learning isnecessary, the learning processor 4071 returns to step 501 to re-acquirelearning data from the learning samples or to add learning samples andacquire new learning data. After the judgment in step 521, if it isfound in step 544 that additional learning is unnecessary, the learningprocessor 4071 executes step 522, as will be detailed later, to judgewhether the image characteristic quantities require adjustment. If theadjustment of the image characteristic quantities is necessary, thelearning processor 4071 conducts image characteristic quantityselections and/or weight adjustments thereof in step 523 and thenreturns to step 506 to re-learn the estimation engine by using adjustedimage characteristic quantities.

The present invention is characterized particularly in that part or allof the various reliability data calculated in steps 508, 509, 510 of thelearning process step (500) is presented from, for example, the GUI ofthe display 409 to the user in step 523.

The present invention is characterized in that the reliability of thepattern cross-sectional shape estimation results that was calculated inthe estimation result reliability calculation step (533) of theperformance process steps (550) is also presented from, for example, theGUI of the display 409 to the user in step 538. Since the reliability ofthe pattern cross-sectional shape estimation results that was thuscalculated in step 533 is presented to the user, it becomes possible forthe user to perform more appropriate judgments on the estimationresults.

Using various reliability data in the learning process step (500) of thesemiconductor pattern cross-sectional shape estimating technique of thelearning type in accordance with the process flow described above makesit possible to judge whether sufficient learning data has been acquiredfor obtaining the process parameter estimation accuracy required.

In the performance process step (550), the reliability of the patternshape estimation results that was obtained in step 538 can also becalculated, and the user can perform more appropriate judgments on theestimation results, based on the calculated reliability.

(Simultaneous Calculation of a Cross-Sectional Shape and ProcessParameters)

Next, a method of estimating a cross-sectional shape and processparameters of a semiconductor pattern simultaneously in the presentinvention to detect a possible abnormality of the semiconductor patternin cross-sectional shape and undertake appropriate countermeasuresagainst the abnormality will be described below using FIG. 6. Thecross-sectional shape and the process parameters are estimated using thesame methods as those described in FIGS. 4 and 5, that is, the learningtype of technique.

For example, the learning processor 4071 of theimage-processing/arithmetic processing unit 407 predetermines, andpre-registers in the database 408, an estimation engine and learningdata 311 for cross-sectional shape estimation, and an estimation engineand learning data 531 for process parameter estimation, in the learningprocess steps (300) and (500).

Next, in performance process step (600), a SEM image of a pattern to bemeasured is acquired from the CD-SEM 401 (420, 421) and then in step 601(329, 529), the SEM image is stored into the database 408, for example.The performance processor 4072 then calculates image characteristicquantities from the acquired SEM image of the pattern in step 602 (330,530). After this, the performance processor 4072 calculates patterncross-sectional shape estimation results 332, cross-sectional shapeestimation result reliability 333, pattern process parameter estimationresults 532, and process parameter estimation result reliability 533,from the above-registered estimation engines and learning data (311,531). Next, the image-processing/arithmetic processing unit 407, forexample, uses the calculated pattern cross-sectional shape estimationresults 332 and cross-sectional shape estimation result reliability 333to execute pattern cross-sectional shape evaluation step 339 describedbelow.

Pattern cross-sectional shape evaluation step 339 is conducted to judgewhether the pattern cross-sectional shape estimation results 332 satisfydesign standards and whether the cross-sectional shape estimation resultreliability 333 are equal to or greater than the foregoing thresholdlevel and the estimation results are reliable enough. If cross-sectionalshape evaluation results on the pattern satisfy the conditions describedlater, the image-processing/arithmetic processing unit 407, for example,transmits an appropriate signal to a process management apparatus (notshown), which then conducts management for the pattern to be transferredto a next process site in step 341. Next, if the cross-sectional shapeevaluation results on the pattern do not satisfy the design standards,the image-processing/arithmetic processing unit 407, for example,executes step 610, as will be detailed later, to calculate parameteradjustment data of the process apparatus (e.g., the exposure machine 702or the etching apparatus 704) from the pattern process parameterestimation results 532 that were calculated together with the aboveevaluation results. If the process parameter estimation resultreliability 533 is judged to be equal to or greater than a thresholdlevel and the pattern process parameter estimation results are judged tobe reliable enough, step 611 is executed to feed back the data to theprocess in which the pattern was formed (e.g., mask design process 701,exposure process 702, or etching process 704).

As described above, since the process parameters with which thesemiconductor pattern was formed are estimated simultaneously with thecross-sectional shape of the pattern, if the cross-sectional shape isevaluated and does not satisfy the design standards (i.e., if anabnormality is detected), feedback of the adjustment data to the processbecomes possible by calculating the data from the process parameterestimation results 532.

(Example of Process Management)

Next, a method of semiconductor-manufacturing process monitoring(management) based on cross-sectional shape estimation of semiconductorpatterns and on reliability of cross-sectional shape estimation results,and more particularly, a process flow of feedback to a process will bedescribed below using FIG. 7. As described in FIGS. 4 and 5, across-sectional shape or process parameters of a pattern to be measuredcan be calculated from a SEM image of the pattern. Although calculationresults on the cross-sectional shape of the pattern can be presented tothe user through the GUI described later, a description will be givenbelow of an example of automatic process management using the calculatedcross-sectional shape information and process parameters of the pattern.FIG. 7 is an explanatory diagram of the process flow of semiconductorprocess management according to the present invention, showing anexample of the process flow of monitoring the cross-sectional shape orprocess parameters of the pattern formed in an exposure process oretching process.

A section surrounded with a broken line in FIG. 7 denotes a flow ofsemiconductor processes. A circuit pattern is formed by designing anexposure mask (step 701), providing exposure from an exposure machineusing the designed exposure mask (step 702), conducting development witha developing apparatus to form a resist pattern (step 703), and usingthe formed resist pattern to conduct etching with an etcher (step 704).A SEM image of the resist pattern that has been formed after thedevelopment (step 703), or of a gate pattern that has been formed afterthe etching operation (step 704), is acquired using the CD-SEM 401 (420,421), and then in step 720 (329, 529), the SEM image is stored into, forexample, the database 408. The image-processing/arithmetic processingunit 407 calculates image characteristic quantities (described later)from the acquired SEM image in step 721 (330, 530). Next on the basis ofthe calculated image characteristic quantities and the learning data andestimation engine that were registered in the database 408 in step 714(331, 531), the image-processing/arithmetic processing unit 407estimates a cross-sectional shape of the resist pattern or gate patternand calculates reliability of estimation results, in steps 332 and 333,respectively. Alternatively, the image-processing/arithmetic processingunit 407 estimates the process parameters with which the resist patternor the gate pattern was formed (e.g., exposure mask design parameters,exposure and development parameters, or etching parameters), andcalculates reliability of process parameter estimation results, in steps332 and 333, respectively. The image-processing/arithmetic processingunit 407, for example, executes steps 339, 539 to judge whether thecalculated cross-sectional shape estimation results or process parameterestimation results stay within a desired design standard range andwhether respective reliability data calculations 332, 333 are up to orabove the foregoing threshold level and/or satisfy other necessaryconditions. If it is found in steps 341, 541 that the conditions aresatisfied, the image-processing/arithmetic processing unit 407, forexample, transmits an appropriate signal to a process managementapparatus (not shown), which then conducts management for the pattern tobe transferred to a next process site in step 730.

Also, if it is found in step 740 that the cross-sectional shapeestimation results fall outside the standard range and that associatedreliability is equal to or above the threshold level, theimage-processing/arithmetic processing unit 407, for example, selects afeedback destination process site in step 735. After this, theimage-processing/arithmetic processing unit 407, for example, calculatesexposure parameter adjustment data of the exposure machine in step 732and feeds back the calculated exposure parameter adjustment data to theexposure process site 702 of the exposure machine via the network 400 instep 707, or calculates etching parameter adjustment data of the etcherin step 734 and feeds back the calculated etching parameter adjustmentdata to the etching process site 704 of the etcher via the network 400in 733, or calculates mask design data correction data of a mask designapparatus in step 741 and feeds back the calculated mask design datacorrection data to the mask design process site 701 of the mask designapparatus via the network 400 in step 706.

Additionally, if it is found in step 725 that the process parameterestimation results fall outside the standard range and that associatedreliability is equal to or above the threshold level, theimage-processing/arithmetic processing unit 407, for example, selects afeedback destination process site in step 735. After this, theimage-processing/arithmetic processing unit 407, for example, calculatesexposure parameter adjustment data of the exposure machine in step 732and feeds back the calculated exposure parameter adjustment data to theexposure process site 702 of the exposure machine via the network 400 instep 707, or calculates etching parameter adjustment data of the etcherin step 734 and feeds back the calculated etching parameter adjustmentdata to the etching process site 704 of the etcher via the network 400in 733, or calculates mask design data correction data of a mask designapparatus in step 741 and feeds back the calculated mask design datacorrection data to the mask design process site 701 of the mask designapparatus via the network 400 in step 706.

The calculation of the exposure parameter adjustment data in step 732,the calculation of the etching parameter adjustment data in step 734,and the calculation of the mask shape correction data in step 741 may beconducted at the process apparatus side through access to the database408.

Thus, the cross-sectional shape or process parameters of the pattern canbe estimated or monitored in the exposure process or the etchingprocess, respectively. The procedure laid down above relates to anexample of a process management system based on estimating thecross-sectional shape or process parameters of the pattern from the SEMimage thereof. This system configuration enables the process managementusing the cross-sectional shape information of the formed pattern, suchprocess management being a technique that has not been traditionallyachievable.

(Cross-Sectional Shape Information)

Next, details of the information obtained during cross-sectional shapeestimation of semiconductor patterns in the present invention aredescribed below using FIGS. 8A and 8B. As shown in FIG. 8A, estimateditems on a line pattern are, for example, pattern height 804 fromportion 809 to portion 808, TOP-CD 801, Middle-CD 802, and Bottom-CD 803that are line width information, a quantitative value 805 indicative ofa round corner shape, a quantitative value 806 indicative of a skirtshape, and a quantitative value 807 indicative of a pattern sidewallshape. It becomes possible, by enabling these items to be estimated, tomeasure various shapes of patterns such as the normal pattern in FIG.2A, the forward tapered pattern in FIG. 2B, the inverse tapered patternin FIG. 2C, the bowing pattern in FIG. 2D, the top-rounding pattern inFIG. 2E, the overhung pattern in FIG. 2F, the skirt-like pattern in FIG.2G, and the notched pattern in FIG. 2H. As shown in FIG. 8B, estimateditems on a hole pattern are, for example, hole diameter 811 of an upperportion of the hole, hole diameter 812 of a central portion of the hole,hole diameter 813 at the bottom of the hole, and hole diameter in anarbitrary vertical position of the hole, or depth of the hole, or otherdimensions. Reference number 810 denotes the depth of the hole.According to the present invention, cross-sectional shapes of othervarious patterns formed during semiconductor-manufacturing processes canalso be measured.

(Image Characteristic Quantities)

The image characteristic quantities used in the present invention have acorrelation with three-dimensional geometric changes in pattern, andpart or all of the image characteristic quantities discussed in JapanesePatent Application No. 2005-320319. The above-mentioned imagecharacteristic quantities include MPPC (Multiple Parameters ProfileCharacterization) image characteristic quantities, tilt MPPC imagecharacteristic quantities, differential tilt MPPC image characteristicquantities, image characteristic quantities based on texturalinformation, and image characteristic quantities based on line profileanalysis. The image characteristic quantities that can be used in thepresent invention, however, are not limited to the above and theinvention makes it possible to select image characteristic quantitiesapplicable to estimating the cross-sectional shapes or processparameters described above.

A description based on FIGS. 9A and 9B is given below of an example of amethod in which the image-processing/arithmetic processing unit 407, forexample, executes steps (305, 505; 330, 530) to calculate imagecharacteristic quantities indicative of the pattern cross-sectionalshape or process parameters or of device characteristics or the like,from the SEM image of a learning sample or a pattern to be measured,acquired from the CD-SEM 401 (420, 421) or the like. An imagecharacteristic quantities calculation range 903 is extracted from theSEM image 901 of the learning sample or to-be-measured pattern, shown inFIG. 9A. Next, the line profile 904 shown in FIG. 9B is created andvarious image characteristic quantities effective for calculating thecross-sectional shape of the pattern are calculated from the createdline profile.

Next, a detailed process flow of the calculation is described below.First as shown in FIG. 9A, the image characteristic quantitiescalculation range 903 required for the creation of the line profile isspecified in the SEM image 901. For example, if the pattern (902) is aline pattern extending in Y-axially (in a vertical direction of thedrawing) across a field of view of the SEM image, the imagecharacteristic quantities calculation range 903 is a range in which atleast sections for calculating the image characteristic quantities areall encompassed X-axially (in a horizontal direction of the drawing).This range also contains the number of pixels (primary-electron scanlines) required to average pixel values of X-coordinates in the Y axialdirection in order to reduce noises due to the SEM image. For example,if the line pattern 902 extending in a Y-direction is the pattern to bemeasured, an image range containing a plurality of pixels (e.g., 100pixels) is selected on the SEM image 901 shown in FIG. 9A. At this time,characteristic noise components of the SEM image can be reduced if thenumber of pixels used for pixel data averaging is large enough. Theselection range in the Y-direction can be changed, as appropriate,according to the shape of the pattern measured.

Next, the pixel data (signal strength value) of the X-coordinates isaveraged Y-axially in the selected pixel range and thus an X-axial lineprofile is created. Execution of processing in up to this process stepcreates the line profile (910) in the image characteristic quantitiescalculation range 903 of the pattern. Next, image characteristicquantities corresponding to various dimension information such as linewidth of the pattern and edge width thereof are calculated from theabove-created line profile (910). Upper and lower graphs in FIG. 9B showa relationship between the cross-sectional shape (905) and the lineprofile (910). The line profile (910) represents the secondary electronstrength obtained from the SEM image. In general, the secondary electronstrength increases according to a tilt angle of the pattern measured, sothe signal strength at sidewalls 907, 908 of the pattern increases abovethat of a planar section 906. Band-like linear sections formed byincreases in the secondary electron strength at the sidewalls and/orother portions of the pattern are called white bands. The various imagecharacteristic quantities shown in the lower graph of FIG. 9B arecalculated as the image characteristic quantities indicating the patterncross-sectional shape of the pattern.

That is to say, bottom width 911 of the pattern, as one of the variousimage characteristic quantities mentioned above, indicates a tendencyfor the cross-sectional shape of the line pattern to change in width ata bottom section, top width 912 of the pattern, as another imagecharacteristic quantity, indicates a tendency for the cross-sectionalshape of the line pattern to change in width at a top section, peakwidth 913 of the line profile, as yet another image characteristicquantity, indicates a tendency for the cross-sectional shape of the linepattern to change in width at a vertical middle section, average width914 of the inside of the right-side white band indicates roundness of atop section at the right side of the cross-sectional shape of the linepattern, average width 915 of the inside of the left-side white bandindicates roundness of a top section at the left side of thecross-sectional shape of the line pattern, average width 916 of theoutside of the right-side white band indicates a shape of a bottomsection at the right side of the cross-sectional shape of the linepattern, average width 917 of the outside of the left-side white bandindicates a shape of a bottom section at the left side of thecross-sectional shape of the line pattern, right-side white band width918 indicates a tendency for the right sidewall of the cross-sectionalshape of the line pattern to change in width, and left-side white bandwidth 919 indicates a tendency for the left sidewall of thecross-sectional shape of the line pattern to change in width.

Next, tilt MPPC image characteristic quantities are described below. Forthe characteristic quantities that were calculated using the lineprofile created from the foregoing SEM image, since only a top-downimage of the pattern is used to acquire cross-sectional shapeinformation thereof, sidewall shapes, height information, or footingshape of a line pattern, for example, may not be properly observablebecause of the pattern shape. Accordingly, a description based on FIG.10 will be given hereunder of a method in which the image characteristicquantities indicating the cross-sectional shape of the pattern can becalculated, even under the above situation, by using the tilt SEM imagediscussed in the description of the foregoing CD-SEM.

As discussed in the description of the CD-SEM configuration, severalways are available to obtain the tilt SEM image. For simplicity, adescription is given below assuming that a relatively inclined pattern1005 is irradiated with SEM electrons 1020 from above. In this case,since the pattern 1005 is inclined, a large number of regions at a rightsidewall 1007 of the line pattern (1005) are irradiated with electronbeams. Consequently, a white band 1018 at the right sidewall side,defined by the right sidewall 1007, becomes thick, compared with thewhite band in the top-down SEM image. Conversely, at a left sidewall1008 of the line pattern 1005, the number of regions irradiated with theelectron beams is small, so a white band 1019 at the left sidewall sidebecomes thin, compared with the white band in the top-down SEM image.

In this way, inclining the pattern with respect to an irradiatingdirection of the electron beams makes it possible to expand an observingregion for the right sidewall of the line pattern 1005 and thus toobserve this sidewall in more detail than in the top-down SEM image.Image characteristic quantities for acquiring cross-sectional shapeinformation from the tilt SEM image can be calculated by calculating,from a line profile 1010 obtained from the tilt SEM image, imagecharacteristic quantities 1011-1019 similar to the MPPC characteristicquantities 911-919 shown in FIG. 9B.

Next, differential tilt MPPC image characteristic quantities aredescribed below. Using the tilt MPPC image characteristic quantities1011-1019 as described above makes it possible to obtain bettercalculation results on the cross-sectional shape, than those obtainedusing only the MPPC characteristic quantities 911-919 of the top-downSEM image. However, the image characteristic quantities indicating thecross-sectional shape of the pattern can likewise be calculated by usingvariations in the image characteristic quantities calculated atdifferent tilt angles (hereinafter, these image characteristicquantities are called the differential tilt MPPC image characteristicquantities). An example in which the differential tilt MPPC imagecharacteristic quantities become effective for calculating thecross-sectional shape of the pattern is described below using FIGS. 11Aand 11B. A pattern of a normal cross-sectional shape is shown as patternA (1101) in FIG. 11A, and a pattern reduced in height is shown aspattern B (1102) in FIG. 11B. Since pattern A has its MPPC imagecharacteristic quantities and its tilt image characteristic quantitiescalculated using a tilt image as described above, the right-sidewallwhite band of the tilt MPPC image characteristic quantities becomesthick, compared with that of an associated top-down SEM image, and theleft-sidewall white band of the tilt MPPC image characteristicquantities becomes thin, compared with that of the top-down SEM image.However, for a pattern reduced in height, such as pattern B, even when atilt SEM image thereof is used, a differential value between theright-sidewall white band of the tilt MPPC image characteristicquantities in the tilt SEM image and the right-sidewall white band ofthe MPPC image characteristic quantities in an associated top-down SEMimage does not change, compared with a differential value of pattern A.The same also holds true for the left-sidewall white bands in both SEMimages. These are due to the fact that since the sidewalls of pattern Bare reduced in height, even if an observing region for the sidewalls ofthe pattern is expanded on the tilt image, the expansion does not appearas increases in widths of the white bands. The white-band widths ofpattern A in the differential tilt MPPC image characteristic quantities,therefore, take a larger value than the white-band widths of pattern Bin the differential tilt MPPC image characteristic quantities. Thedifferential tilt MPPC image characteristic quantities discussed hereare an example of image characteristic quantities effective forcalculating the three-dimensional shapes of the patterns which wereobtained from the tilt images formed at different tilt angles.

Next, image characteristic quantities based on textural analysis aredescribed below. Specifically, a method of calculating imagecharacteristic quantities effective for cross-sectional shapecalculation of a pattern, from a SEM image of the pattern, is describedas an example below using FIGS. 12A and 12B. The image characteristicquantities described here are characterized in that two-dimensionalinformation within an image region which contains the pattern iscalculated from the SEM image thereof. A method of calculating imagecharacteristic quantities effective for cross-sectional shapecalculation of the pattern is described below as an example ofcalculating the above image characteristic quantities. As shown in FIG.12A, in this calculation method, a textural analysis region 1112 to besubjected to textural analysis of the pattern is specified in a SEMimage 1111. The textural analysis region 1112 is specified so that atleast the pattern is included in the region. An example of the texturalanalysis method is by creating a frequency distribution 1113 of signalstrength within the textural analysis region 1112, then calculating theimage characteristic quantities that indicate a shape of the frequencydistribution 1113, and taking calculation results as the imagecharacteristic quantities of the pattern. The image characteristicquantities indicating the shape of the frequency distribution include,for example, an average, variance, skewness, and kurtosis.

When signal strength “i” has its frequency expressed as P(i), each imagecharacteristic quantity is given by expression (1). $\begin{matrix}\begin{matrix}{Average} & {\mu = {\sum\limits_{i = 0}^{n - 1}{{iP}(i)}}} \\{Variance} & {\sigma^{2} = {\sum\limits_{i = 0}^{n - 1}{\left( {i - \mu} \right)^{2}{P(i)}}}} \\{Skewness} & {S = {\sum\limits_{i = 0}^{n - 1}{\left( {i - \mu} \right)^{3}{{P(i)}/\sigma^{3}}}}} \\{Kurtosis} & {K = {\sum\limits_{i = 0}^{n - 1}{\left( {i - \mu} \right)^{4}{{P(i)}/\sigma^{4}}}}}\end{matrix} & {{Expression}\quad(1)}\end{matrix}$

For example, if the pattern has its top portion formed into a wavyshape, not a planar shape, by the process parameters used for thesemiconductor, the skewness and kurtosis that are texturalcharacteristic quantities calculated from a frequency distribution 1116of signal strength within a textural analysis region 1115 of a SEM image1114 will, as shown in FIG. 12B, be smaller than in a SEM image 1111 ofa pattern whose top is planar. Using such textural characteristicquantities as shown above provides useful information for understandinga tendency that the cross-sectional shape of the pattern exhibits. Thecharacteristic quantities calculated from the frequency distribution ofthe SEM signal strength in the textural analysis discussed above are anexample of image characteristic quantities effective for analyzing thecross-sectional shape of the pattern.

Next, notch detection image characteristic quantities based on lineprofile analysis are described below. FIGS. 13A to 13D are diagramsexplaining examples of image characteristic quantities effective forcross-sectional shape detection of a pattern from a SEM image thereof.The above-mentioned line profile obtained from the SEM image exhibits aspecific tendency due to the cross-sectional shape of the pattern. Thetendency of the line profile is analyzed and results are calculated asimage characteristic quantities. Taking these image characteristicquantities as an example, a description based on FIGS. 13A-13D is givenbelow of the image characteristic quantities that render a notched shape1123 of a resist pattern detectable. FIGS. 13A, 13B show cross-sectionalshapes of different line patterns. FIG. 13A shows a line pattern of anormal cross-sectional shape 1121, and FIG. 13B shows a line pattern ofan abnormal cross-sectional shape 1122 curved inward at bottom 1123 withrespect to a vertical line. Such an abnormal cross-sectional shape withbottom 1123 is called a notched shape.

In comparison between line profiles obtained from SEM images of thepatterns in FIGS. 13A, 13B, the line profile of the pattern's rightsidewall that is associated with the notch 1123 in FIG. 13B, that is,line profile 1125 in FIG. 13D has a tendency for a base 1126 of amountain of the line profile to decrease in signal strength, comparedwith the line profile 1124 shown in FIG. 13C corresponding to thepattern's right sidewall of the normal line pattern 1121 in FIG. 13A.Such a tendency is considered to be caused by an electrical charge stateof the pattern due to the cross-sectional shape thereof, and by abehavior of secondary electrons due to the electrical charge. Thetendency for the base 1126 of the mountain of the line profile todecrease in signal strength is calculated as an image characteristicquantity here. During the calculation of the image characteristicquantity, a differential 1127 in SEM signal strength between anunderlayer and notch of the pattern under observation is calculated asan example of the image characteristic quantity. Using the tilt SEMimage, in particular, that has been discussed in the description of theforegoing CD-SEM makes it possible to acquire the SEM image on which anedge effect is observed at the notch 1123 of the line pattern bottom, byirradiating the notch directly with electrons from the SEM, and tocalculate the image characteristic quantity indicating a degree of thenotch, by analyzing the line profile of the pattern.

Next, overhang detection image characteristic quantities are describedbelow. FIGS. 14A to 14F are diagrams explaining examples of imagecharacteristic quantities effective for cross-sectional shape detectionof a pattern from a SEM image thereof. The above-mentioned line profileobtained from a tilt SEM image exhibits a specific tendency due to thecross-sectional shape of the pattern. The tendency of the line profileis analyzed and results are calculated as image characteristicquantities. FIG. 14A shows a cross-sectional shape 1131 of a patternhaving inverse tapered sidewalls, and this shape is called an overhungshape. FIG. 14B shows a cross-sectional shape 1134 of a normal pattern.

FIGS. 14C-14F respectively show a line profile 1137 calculated from aSEM image of an overhung pattern when the pattern is observed intop-down view (1137), a line profile 1138 calculated from a tilt imageof the pattern in a tilt condition (1133), a line profile 1139calculated from a SEM image of a normal pattern when the pattern isobserved in top-down view (1135), and a line profile 1140 calculatedfrom a tilt image of the normal pattern in a tilt condition (1136).

There is almost no difference between the profiles 1137 and 1139calculated from respective top-down SEM images. However, in comparisonbetween the profiles 1138 and 1140 calculated from respective tilt SEMimages, the line profile 1140 of the normal pattern 1134 exhibits athick white band at either left or right as described above (in FIG.14F, the white band at the right sidewall is thick). In contrast tothis, the overhung pattern 1131 has a tendency not to exhibit thickwhite bands in the line profile 1138 at up to a certain tilt angle,because of the occurrence of the electrical charge of the pattern andbehavior of secondary electrons due to the pattern shape.

Image characteristic quantities that indicate these differences betweenthe line profiles of the normal pattern 1134 and overhung pattern 1131are calculated and calculation results are taken as image characteristicquantities for use in cross-sectional shape calculation of the pattern.These image characteristic quantities calculated from line profilesinclude, for example, the foregoing tilt MPPC image characteristicquantities. The MPPC image characteristic quantities of the lineprofiles obtained from tilt SEM images during imaging of the patternsdescribed above are an example of image characteristic quantitieseffective for calculating the cross-sectional shape of the overhungpattern, and using the image characteristic quantities obtained from theline profiles created from tilt SEM images due to various suchcross-sectional pattern shapes makes it possible, during the calculationof a cross-sectional pattern shape, to obtain better calculation resultson the cross-sectional shape.

The above-described top-down MPPC image characteristic quantities, tiltMPPC image characteristic quantities, differential tilt MPPC imagecharacteristic quantities, image characteristic quantities based ontextural analysis, notch detection image characteristic quantities basedon line profile analysis, and overhang detection image characteristicquantities are effective during cross-sectional pattern shapecalculation of the learning samples and to-be-measured patternsdescribed in FIGS. 4 to 7. In addition, changes in process parametersappear as changes in the cross-sectional shape of the pattern beingformed, so a tendency of the process parameters can be understood byusing the above-described image characteristic quantities and analyzingthe changes in the cross-sectional shape of the pattern being formed.These image characteristic quantities, therefore, become effectivecharacteristic quantities during cross-sectional pattern shapecalculation of the patterns described in FIGS. 5 to 7. Furthermore,since the device performance of the pattern being formed issignificantly affected by the cross-sectional shape of the pattern, thedevice performance can be estimated by using the above-described imagecharacteristic quantities.

(Estimation Engines)

Part or all of the estimation engines discussed in Japanese PatentApplication No. 2005-320319 can be used as the estimation enginesrelating to the present invention. These estimation engines include, forexample, a k-NN method and a likelihood estimation method. Theinvention, however, is not limited to these estimation engines and makesit possible to select a technique usable for estimating thecross-sectional shapes or process parameters described above.

That is to say, a description is given below of selecting an estimationengine for the estimation items relating to the present invention (i.e.,the cross-sectional shape of the pattern or the process parameters forforming the pattern). An appropriate estimation engine is determined asthe above estimation engine based on the association between theestimation items and image characteristic quantities, which areexpressed by learning data. While an example of the estimation enginesused in the present embodiment will be described hereunder, theseestimation engines are not limited to the embodiment and otherestimation engines can likewise be used. The examples of estimation withan engine, which is described below, employ the likelihood estimationmethod, the k-NN method, or a method based on multiple-regressionanalysis.

Each type of estimation engines has its specific features discussedbelow, and as described above, an appropriate estimation engine isselected according to the particular relationship between estimationitems and image characteristic quantities. If a distribution between theestimation items and the image characteristic quantities has continuityand is essentially free from bias, the likelihood estimation method ormultiple-regression analytical method using a functional equation toprovide the distribution with approximation is suitable. Both methodsare advantageous in that approximation makes them insusceptible to theexceptional value contained in respective learning data.

However, there is the problem that an appropriate functional equationneeds to be set for approximation. Conversely, if the distributionmentioned above is low in continuity and has a significant bias, thek-NN method that does not involve approximation of the distribution witha functional equation is suitable. This method has an advantage in thatit is effective in cases where the approximation with a functionalequation is difficult. This method, however, has the problem that it issusceptible to the exceptional value contained in associated learningdata. With these advantages and problems taken into account, anappropriate estimation engine is selected according to the particularrelationship between estimation items and image characteristicquantities.

Next, a method of estimating a cross-sectional shape or processparameters of a pattern, based on the likelihood estimation method, isdescribed as an example below using FIGS. 15 and 16A to 16C. The exampledescribed below uses the above-mentioned likelihood estimation methodfor the estimation engine. Here, it is assumed that a cross-sectionalshape is estimated. For process parameter estimation, thecross-sectional shape may be replaced with process parameters in thedescription. Although it has been discussed that the likelihoodestimation method is used for the estimation engine in the example,likelihood estimation is not the only method applicable and other typesof estimation engines can be used; there are no limitations, if theabove-mentioned image characteristic quantities of the pattern to bemeasured are used as an input in the cross-sectional shape or processparameter estimating method actually selected.

FIG. 15 shows a method in which learning data for cross-sectional shapeestimation is created in the estimation engine learning process step(306) of the learning process step 300 shown in FIG. 4. FIGS. 16A-16Care diagrams showing a method in which cross-sectional shapes ofpatterns to be measured are calculated by collating the imagecharacteristic quantities that have been calculated from each pattern,with the learning data for cross-sectional shape estimation in thepattern cross-sectional shape estimating step (332) of the performanceprocess step 350 shown in FIG. 4. In the example described below, thenumber of image characteristic quantities for use in cross-sectionalshape estimation is limited to three for simplicity in the description.

In the learning process step 300, SEM images of various cross-sectionalshapes are acquired from various learning samples in the learning dataacquisition step 301, and the learning processor 4071 calculates imagecharacteristic quantities from the acquired SEM images and derives anassociation between each calculated image characteristic quantity andthe cross-sectional shape of each pattern. Upper graphs 1151 to 1153 inFIG. 15 each represent the specific association between each calculatedimage characteristic quantity “mk(t)” and cross-sectional shape “t”(such as pattern height) of the pattern, plotted with thecross-sectional shape taken on a horizontal axis and the imagecharacteristic quantity (m1, m2, m3) on a vertical axis. Next as shownin lower graphs 1154 to 1156 of FIG. 15, the upper graphs 1151 to 1153in FIG. 15 are smoothed to create the learning data (model data “Mk(t)”)that associates the cross-sectional shape “t” of the pattern and theimage characteristic quantity (m1, m2, m3). The learning data is createdfor each image characteristic quantity, with “Mk(t)” as a functionidentifying the learning data, “t” as a value identifying thecross-sectional shape, “k” (k=1 . . . n) identifying the imagecharacteristic quantity, and “n” denoting the number of imagecharacteristic quantities. The calculated learning data is temporarilyregistered in the database 408 in step 306. After this, reliability iscalculated in step 307 and then the calculated reliability is used toevaluate learning states, estimation engines, and estimation results,determine the estimation engine and learning data satisfyingpredetermined data criteria, and register the determined estimationengine and learning data in the database 408.

In the performance process step 350, a SEM image of the pattern to bemeasured is acquired and then the performance processor 4072 calculatesimage characteristic quantities from the acquired SEM image in step 330and estimates the cross-sectional shape of the pattern in step 332 bycollating the calculated image characteristic quantities with thecross-sectional shape estimation engine and learning data registered inthe database 408. Values of the image characteristic quantities M1, M2,M3 that have been calculated from the SEM image of the pattern areexpressed as f1, f2, f3, respectively, in FIG. 16A. Suppose that asshown in FIG. 16A, the values f1, f2, f3 of the image characteristicquantities are equivalent to 1164, 1165, 1166 on the three sets oflearning data, 1161, 1162, 1663. Also, suppose that a variation in imagecharacteristic quantity “fk” complies with a normal distribution ofstandard deviation “ρk”. The likelihood function “pk(t)” (k=1 . . . n)shown in expression (2) is calculated on the suppositions.pk(t)=1/√{square root over (2π)}=exp(−(fk−Mk(t))²/2σk)  Expression (2)where “pk(t)” is a value indicating that the cross-sectional shape (suchas pattern height) exhibits a probability of “t”. A value appropriatefor actual variations in process parameters associated with the imagecharacteristic quantity “fk” is given as “ρk”. Examples of a calculatedlikelihood function are shown as graphs 1167, 1168, 1169 in FIG. 16B. Asthe likelihood in each image characteristic quantity increases, thelikelihood indicates a cross-sectional shape closer to that of thepattern under measurement. As shown in expression (3), multiplicationsare performed with the likelihood distributions (p1(t), p2(t), . . .pn(t)) that have been calculated from each image characteristicquantity. The cross-sectional shape having the greatest value in FIG.16C, that is, cross-sectional shape 1170 with “maxP(j)” takes the value“t” that indicates the cross-sectional shape of the pattern, as shown inexpression (4). $\begin{matrix}{{P(t)} = {p\quad 1(t) \times p\quad 2(t) \times {\bigwedge{\times {{pn}(t)}}}}} & {{Expression}\quad(3)} \\{t = \left\{ {{t\text{|}{P(t)}} = {\max\limits_{j}{P(j)}}} \right\}} & {{Expression}\quad(4)}\end{matrix}$

Next, a method of estimating a pattern cross-sectional shape or processparameters with multiple-regression analysis is described as an examplebelow. In the estimation method based on multiple-regression analysis,the desired cross-sectional shape of the pattern is calculated from thesum obtained by multiplying weights suitable for estimating thecross-sectional shape, that is, regression variables (a, b1, b2, . . . )for each image characteristic quantity that was calculated from the SEMimage of the pattern. The regression variables are calculated from theimage characteristic quantities (x1, x2, . . . ) of the SEM images ofthe various learning samples used in step 306 (creation of learning datafor cross-sectional shape estimation) of the learning process step 300in FIG. 3. The thus-created multiple-regression equation is registeredin the database 408 as the learning data for cross-sectional shapeestimation. An example of the multiple-regression equation used is shownin expression (5) or the like.y=a+b1x1+b2x2+  Expression (5)where “y” is an object variable denoting the cross-sectional shape ofthe pattern, such as pattern height, and “x1” and “x2” are descriptivefunctions each denoting the image characteristic quantity (such as linewidth characteristic quantity) that was calculated from the SEM image ofthe pattern. Also, “a”, “b1”, and “b2” are the weights suitable forestimating the cross-sectional shape, and these weights are multipliedby the above-calculated image characteristic quantities stored withinthe database 408, for example, and are each a constant term (i=1, 2, . .. , n), where “n” is a total number of image characteristic quantities.

In the performance process step 350, image characteristic quantities arecalculated from the SEM images of the pattern to be measured, and thenthe cross-sectional shape of the pattern is calculated by applying eachcalculated characteristic quantity to the learning data forcross-sectional shape estimation, shown in the multiple-regressionequation of expression (5).

Next, the cross-sectional shape or process parameter estimation of apattern that uses the k-NN method is described as an example below usingFIGS. 17 and 18. FIGS. 17 and 18 are diagrams that explain estimationwhich uses the k-NN method as the above-mentioned estimation engine inan example of estimating a cross-sectional shape or process parametersof a semiconductor pattern, in which example, pattern height 804 isestimated as an index value of the cross-sectional shape of the patternshown in FIG. 8A. For process parameter estimation, the cross-sectionalshape may be replaced with process parameters in the description.Although it has been discussed that the k-NN method is used as theestimation engine in the example, this method is not the only methodapplicable and other types of estimation engines can be used; there areno limitations, if the above-mentioned image characteristic quantitiesof the pattern to be measured are used as an input in thecross-sectional shape or process parameter estimating method actuallyselected.

FIG. 17 is a process flow diagram of estimating a cross-sectional shapeor process parameters of a pattern using the k-NN method. In thismethod, a combination between image characteristic quantities andcross-sectional shapes of patterns of various learning samples(cross-sectional shapes) which have been determined from evaluationsbased on reliability calculation is registered in step 331 as thelearning data for cross-sectional shape estimation, shown in FIG. 4.That is to say, this method, unlike the likelihood estimation method,does not include creating the function that identifies learning data.After the above registration, a SEM image of the pattern is acquired instep 329 and then image characteristic quantities are calculated fromthe acquired SEM image in step 330. Next in pattern cross-sectionalshape estimating step 332, a “k” number of learning samples closest tothe pattern to be measured, in an associated image characteristicquantities space, is selected in substep 3321. An interpolation valuebased on displacement vectors between the pattern and each learningsample is calculated in substep 3322 for the cross-sectional shapes(such as pattern height) of the selected “k” number of learning samplesclosest to the pattern to be measured, and the calculated value isdefined as an estimation value of the cross-sectional shape (e.g.,height) of the pattern to be measured, in substep 3323. The value of “k”here can be any value ranging from 1 to the total number of learningsamples, and is defined according to a particular distribution state ofthe learning samples in the image characteristic quantities space.

FIG. 18 is a conceptual diagram that shows the selection of a “k” numberof learning samples closest the pattern to be measured, in the imagecharacteristic quantities space, in substep 3321. In this diagram, thenumber of image characteristic quantities is taken as nine (f=(f1, f2,f3, . . . , f9)^(T)), and the learning samples 1180 that were registeredin a learning process step are distributed in the image characteristicquantities space.

Next, a “k” number of learning samples closest to the pattern to bemeasured in terms of distance “d(f, f′)”, which is the distance from thepattern to be measured, in the image characteristic quantities space,are selected on the basis of the image characteristic quantities (f=(f1,f2, f3, . . . , f9)^(T)) that were calculated from the pattern. Distance“d(f, f′)” is given as a Euclidean distance by expression (6).$\begin{matrix}{{d\left( {f,f^{\prime}} \right)} = \sqrt{\sum\limits_{j = 1}^{9}\left( {{fj} - {fj}^{\prime}} \right)^{2}}} & {{Expression}\quad(6)}\end{matrix}$

The cross-sectional shape (e.g., height H) of the pattern to be measuredis calculated using an interpolation equation given by expression (7)based on the cross-sectional shapes (e.g., height) of the selected “k”number of learning samples. $\begin{matrix}{H = {{h\quad 0} + {\sum\limits_{j = 1}^{9}{wjfj}^{\prime}}}} & {{Expression}\quad(7)}\end{matrix}$where “wj” (weight) and “h0” are calculated from the selected “k” numberof learning samples, both calculations using the least-square method.

Thus, it becomes possible to estimate the cross-sectional shape (e.g.,pattern height H) of the pattern to be measured.

As described above, based on part or all of the image characteristicquantity data which has been calculated from a SEM image of a pattern tobe measured, estimation of a cross-sectional shape thereof or estimationof the process parameters used to form the pattern can be achieved byconducting a estimation process with learning data (data that consistsof a combination between SEM images and cross-sectional shapeinformation or process parameter information associated with the SEMimages) and with an estimation engine such as the likelihood estimationmethod, multiple-regression analytical method, or k-NN method.

(Reliability of Image Characteristic Quantities)

FIG. 19 is a diagram that explains a learning state evaluation method(311, 511) which, in an estimation technique based on the reliability ofthe cross-sectional shape or process parameter estimating methodaccording to the present invention, uses the reliability (308 in FIG. 4or 508 in FIG. 5) of the above-mentioned image characteristic quantitiescalculated from a SEM image. In this evaluation method, the reliability(308, 508) of the image characteristic quantities can be calculated froma distribution state thereof, and based on the calculated reliability,judgments can be performed in step 321, 521 to determine whetheradditional learning of learning data is necessary, and in step 322, 522to determine whether image characteristic quantities adjustment isnecessary. Image characteristic quantities distribution state analyzingstep 1210 described later is conducted for the distribution state of theimage characteristic quantities that were calculated from the SEM images302, 502 associated with the learning data described in FIGS. 4 and 5(in FIG. 19, denoted as 1200). After the analysis of the imagecharacteristic quantities distribution state, reliability 1202 of theimage characteristic quantities, continuity 1203 thereof, a separationlevel 1204 thereof, learning density 1205 thereof, or model applicationappropriateness 1206 thereof is calculated as the reliability of theimage characteristic quantities. Although the five index values indicatethe distribution state of the image characteristic quantities, the kindsof indicators usable as the index values indicating the distributionstate of the image characteristic quantities are not limited to the fivevalues.

The calculated reliability can be presented to the user in step 313,513, through the GUI described later. Also, the user can use thispresented data to judge whether the image characteristic quantities datadescribed below has been acquired in amounts great enough for obtainingsufficient estimation accuracy in the estimated fluctuation ranges ofeach estimation parameter used. In addition, the user can judge in step321, 521 to determine whether additional learning of learning data isnecessary, and judge in step 322, 522 to determine whether imagecharacteristic quantities adjustment is necessary.

First, based on the calculated reliability, acceptability judgments insteps 1210 to 1214 are performed on the image characteristic quantities.During the acceptability judgments, a threshold level is specified foreach kind of reliability and if the threshold level is satisfied, theimage characteristic quantities are judged to satisfy conditions of thereliability. Conversely if the threshold level is not satisfied, whetheradditional learning of learning data is necessary is judged in step 321,521.

If additional learning is judged to be necessary, the process proceedsto additional learning process step 343, 543. The cross-sectional shapeor process parameters to be subjected to additional learning aredetermined according to the above reliability. Additional learning isperformed on the cross-sectional shape or process parameters whoseestimation result reliability displayed through the GUI is lower thandesign standards, or on the cross-sectional shape or process parameterswhose data tends to decrease. After the additional learning, thelearning state can be confirmed through the GUI once again, and learningcan thus be repeated until the design standards have been met or untilthe user has judged additional learning to be unnecessary.

Judgment step 322, 522 to judge whether image characteristic quantitiesadjustment is necessary follows if additional learning is judged to beunnecessary. If the image characteristic quantities in the learning dataare judged to require adjustment, the process proceeds to imagecharacteristic quantities selection and/or weight adjustment step 323,523. The weight that has been defined in the weight adjustment step isused as the value for weighting the image characteristic quantitiesduring cross-sectional shape estimation or process parameter estimation.In the same manner as that of confirmation during judgment of whetheradditional learning is necessary, the user can set the above weightwhile confirming the reliability of the image characteristic quantitiesvia the GUI. In addition, the estimation engine reliability describedlater and the reliability of the estimation results can also bedisplayed through the GUI, so that the user can set the weight whileconfirming the two kinds of reliability.

During the above judgments on the image characteristic quantities, whenall reliability data is ANDed in step 1210, if all the reliability datais judged to be satisfied (i.e., if the distribution of the imagecharacteristic quantities in the learning data is judged to satisfynecessary conditions), the process proceeds to next step 327 (FIG. 4) or527 (FIG. 5) of the learning process steps (300, 500). Thus, based onthe reliability of the image characteristic quantities that werecalculated from the distribution thereof in the learning data, judgmentscan be conducted to determine whether additional learning is necessaryand whether the adjustment of the image characteristic quantities isnecessary.

FIGS. 20A to 20E are diagrams explaining the reliability of the imagecharacteristic quantities calculated from the distribution thereof inthe learning data. The reliability can be used to judge, duringcross-sectional shape or process parameter estimating, whether thenumber of samples for learning data and/or a distribution of thelearning data suffices to obtain sufficient estimation accuracy in theestimated fluctuation ranges of each estimation parameter used. Whilefive index values (sensitivity, continuity, a separation level, learningdensity, and appropriateness of model application) will be describedhereunder as indicators of reliability, index values that can be usedare not limited to the above five kinds; any index value indicating thedistribution state of the image characteristic quantities in thelearning data and useful for conducting the above judgments on thelearning data can be used as an indicator of the reliability.

An index value 1315 of the reliability, with respect to the sensitivity1202 shown in FIG. 19, is an index value that, as shown in FIG. 20A,denotes magnitude of a change in image characteristic quantity accordingto a change in a cross-sectional shape or process parameters of adistribution 1312 of the image characteristic quantities. Thedistribution range for calculating this index value is an estimatedfluctuation range 1361 that is either a fluctuation range in which thecross-sectional shape is likely to be formed as a result of processchanges, or a fluctuation range in which the process parameters arelikely to become effective data in the formation of the pattern. Thevalue of the sensitivity as the reliability, decreases in a range 1310,where a relative change in characteristic quantity with respect to achange in cross-sectional shape or in process parameters tends to becomeless significant than in another range 1311. In other words, in terms ofreliability index 1315 of the sensitivity to the change incross-sectional shape or in process parameters, reliability of the range1310 where the change in characteristic quantity tends to become lesssignificant decreases as denoted by curve 1313, and reliability of therange 1311 where the change in characteristic quantity tends to becomemore significant increases as denoted by curve 1314.

This means that if the reliability index value of the sensitivity in theimage characteristic quantities is too small, the cross-sectional shapeor the process parameters cannot be calculated accurately, even by usingan appropriate model. When calculated, the magnitude of the change incharacteristic quantity can be defined, for example, as a fluctuationlevel thereof (maximum value−minimum value) (1317) in a fixed range 1316of the cross-sectional shape or process parameters. The method ofdefining the maximum value and the minimum value is an example, and ausable calculation method is not limited, if a fluctuation tendency ofthe characteristic quantity can be understood by using the particularmethod.

An index value 1327 of the reliability, with respect to the continuity1203 shown in FIG. 19, decreases, for example, in a range 1321 asdenoted by curve 1325 in FIG. 20B. In the range 1321, the distributionof the characteristic quantities is discontinuous. Conversely, in ranges1320, 1322 where the distribution of the characteristic quantities iscontinuous, the index value 1327 of the reliability increases as denotedby curves 1324, 1326. For the reliability index value 1327 of thecontinuity, the discontinuous range in which the characteristicquantities decrease indicates that the reliability of the learning datais lowered by an acquisition failure of the learning data or otherfactors. This means that if the index value of the reliability as thecontinuity in the image characteristic quantities is too small, thecross-sectional shape or the process parameters cannot be calculatedaccurately, even by using an appropriate model. The distribution rangefor calculating this index value is the estimated fluctuation range 1361of the cross-sectional shape or of the process parameters.

An index value 1333 of the reliability, with respect to the separationlevel 1204 shown in FIG. 19, is an index value that, as shown in FIG.20C, denotes a variation in image characteristic quantity. Thisreliability value decreases in a range 1330 where there are significantvariations, and decreases in a range 1331 where variations areinsignificant. These mean that if the index value 1333 of thereliability as the separation level in the image characteristicquantities is too small, since the image characteristic quantities varysignificantly for a cross-sectional shape or process parameters, thecross-sectional shape or the process parameters cannot be calculatedaccurately, even by using an appropriate model based on the imagecharacteristic quantities. The distribution range for calculating thisindex value is the estimated fluctuation range 1361 of thecross-sectional shape or of the process parameters.

An index value 1342 of the reliability, with respect to the learningdensity 1205 shown in FIG. 19, is an index value that, as shown in FIG.20D, denotes a distribution of learning data acquisition. Thisreliability value decreases in a range 1340 of an image characteristicquantities distribution with a small amount of or no amount of acquiredlearning data (low learning density), and increases in a range 1341 ofan image characteristic quantities distribution with a large amount ofacquired learning data (high learning density). This means that if theindex value 1342 of the reliability as the learning density in the imagecharacteristic quantities is too small, since the amount of acquiredlearning data is insufficient, the cross-sectional shape or the processparameters cannot be calculated accurately, even by using an appropriatemodel. The distribution range for calculating this index value is theestimated fluctuation range 1361 of the cross-sectional shape or of theprocess parameters.

An index value 1352 of the reliability, with respect to the modelapplication appropriateness 1206 shown in FIG. 19, is an index valuethat, as shown in FIG. 20E, denotes an appropriateness level of modelapplication in calculation of a model to be used for estimating with amulti-valued function assigned to a distribution of image characteristicquantities. The reliability index value 1352 of the model applicationappropriateness decreases when calculation results on theappropriateness level of application of the model (1350) which has beencalculated (selected) for the distribution (1351) of the imagecharacteristic quantities indicate that the appropriateness level of themodel application is low. If the reliability index value 1352 of themodel application appropriateness level is small, this means that thedistribution of the image characteristic quantities correspondinglydeparts from the model used for estimation, and hence that the modelrequires a change (including partial modification) and/or weightadjustment. The distribution range for calculating this index value isthe estimated fluctuation range 1361 of the cross-sectional shape or ofthe process parameters.

The foregoing judgments (evaluations) on the learning data can beconducted by calculating the above-described reliability values thatindicate the distribution of the image characteristic quantities.

(Reliability of Estimation Engine)

Next, a method of cross-sectional shape or process parameters estimationbased on reliability of an estimation engine relating to the presentinvention is described as an example below using FIG. 21. FIG. 21 is adiagram showing a method of cross-sectional shape estimation based onreliability of an estimation engine relating to the present invention.In the invention, as shown in FIGS. 4 and 5, reliability of anestimation engine can be calculated in step 309 or 509 duringcross-sectional shape or process parameter estimation with theestimation engine, and an evaluation based on the calculated reliabilitycan be conducted in step 315 or 515 to judge whether sufficientestimation accuracy is obtainable in estimated fluctuation ranges of thecross-sectional shape or process parameters estimated. That is to say,as described in FIG. 19, reliability values (1402 to 1404) for indices(sensitivity, continuity, separation level, learning density, and modelapplication appropriateness) concerning the number and/or distributionstate of learning data samples for the cross-sectional shape or theprocess parameters are calculated with respect to the relationshipbetween image characteristic quantities “f1, f2, f3, . . . , ” (1401)and cross-sectional shape or process parameter indices.

Each calculated reliability index value is weighted (Wa-Wc . . . ,1405-1407) and then summed up to calculate overall reliability 1408 foreach image characteristic quantity. The calculated overall reliabilityis weighted (W1-W3 . . . ) for each image characteristic quantity andthen summed up to calculate the reliability 1410 of the estimationengine. The weight value defined during weight adjustment of the imagecharacteristic quantity is used as a weighting value for the imagecharacteristic quantity when the cross-sectional shape or the processparameters are estimated.

The above method of calculating the overall reliability and theestimation engine reliability is an example and does not limit thepresent invention, and any method can be used that enables thecalculation of the reliability. As described in FIGS. 4 and 5, whetherthe reliability 1410 of the estimation engine satisfies a set thresholdlevel is judged in judgment (evaluation) step 315, 515 for theestimation engine, and if the threshold level is not satisfied,selection of another estimation engine and/or weight adjustment of thepresent estimation engine is conducted in step 319, 519. The reliabilityof the estimation engine can be presented to the user through the GUI instep 313, 513, and the user can perform the above adjustment whileconfirming the reliability via the GUI.

(Reliability of Estimating Results)

FIGS. 22A to 22C are diagrams explaining a method in which thereliability (310, 510; 333, 533) of estimation results, calculated inthe learning process steps 300, 500 and the performance process steps350, 550, is used in a cross-sectional shape estimation technique usingthe reliability of the cross-sectional shape or process parameterestimation method according to the present invention.

During estimation with the foregoing k-NN method, as described inJapanese Patent Application No. 2005-320319, a desired cross-sectionalshape or desired process parameters are estimated using the distancebetween the learning data (data that consists of a combination of SEMimages and cross-sectional shape or process parameter informationassociated with the SEM images) in the image characteristic quantitiesspace, and the subject to be estimated (the pattern measured for eachestimation sample extracted arbitrarily and successively from learningsamples in the learning process steps (300; 500), or in the performanceprocess steps (350; 550)). In this estimation method, the Euclideandistance, for example, between each set of learning data and the subjectto be estimated, is calculated, a “k” number of sets of learning dataclosest to the subject to be estimated (each estimation sample or thepattern to be measured) in terms of the distance are selected, and aprocess such as interpolation based on expression (7) or the like isconducted using each selected set of learning data to calculate thecross-sectional shape or process parameters (or others) of the subjectto be estimated. During the interpolation, the cross-sectional shape orprocess parameters, for example, are calculated by assigning a weightvalue (wj) to each cross-sectional shape or process parameter value ofthe selected learning data according to the particular distance. In thistechnique, basically, as the distance between the subject to beestimated (estimation sample or the pattern to be measured) is shorter,estimating results higher in reliability can be obtained when thecross-sectional shape or process parameters are estimated using the k-NNmethod, one of estimation engines, on the basis of the imagecharacteristic quantities of the subject to be estimated (estimationsample or the pattern to be measured). Accordingly, the above-mentioneddistance is used as an example of reliability of the estimation results.

In FIG. 22A, a number of the subject to be estimated (estimation sampleor the pattern to be measured) is shown on a horizontal axis, and thedistance to the subject to be estimated is shown on a vertical axis. Inthe present example, there exists a subject 1501 to be estimated havingthe abovementioned distance with respect to a distribution 1503 of adistance from a large majority of subjects 1502 to be estimated to thesubject to be estimated in the learning data. The reliability of theestimation results obtained from the subject 1501 to be estimated insuch a learning sample decreases for the reasons discussed above. As inthe present example, therefore, if the distance to the subject to beestimated in the learning sample is long, calculations are conducted forreduced reliability of the estimation results. The reliability of theestimation results can be, for example, a reciprocal of the distance ora square of the reciprocal of the distance. If the above subject to beestimated is used as a measurement subject, the reliability of theestimation results with respect to the measurement subject will becalculated in step 333, 533.

During likelihood estimating, as shown in FIGS. 22B and 22C, in adistribution (1505, 1507) of the likelihood obtained when the parameterestimated (cross-sectional shape or process parameter) changes, a point(1509, 1508) at which the likelihood becomes a maximum is basicallytaken as a solution (cross-sectional shape or process parameter of thesubject to be estimated). Reliability (310, 510; 333, 533) of theestimation results, however, can be calculated from a shape of theparticular likelihood distribution. During likelihood estimating, it isgenerally considered that if the shape of the likelihood distribution issteep (1504), the estimating reliability obtained will increase, andthat if the likelihood distribution is gentle (1506), the estimatingreliability obtained will decrease. Accordingly, a value obtained byquantifying the shape of the likelihood distribution is calculated asthe reliability of the estimation results. For example, a distributionof likelihood is extracted at a certain threshold level (say, about 80%of the likelihood maximum) and a width value (1504, 1506) of theparticular distribution is calculated as the reliability of theestimation results. A calculation range of the reliability can also beextracted only from the estimated fluctuation range (1524, 1527) of thecross-sectional shape or process parameters estimated. Calculation onlyfrom the estimated fluctuation range makes it possible to eliminatecross-sectional shapes which are not formed, or process parameters whichare not set up, before reliability and a solution are calculated.

As described above, the reliability of the estimation results relatingto the subject to be estimated (estimating sample and measurementsubject) is calculated using the selected estimation engine. Acalculation method for the reliability of the estimation results is notlimited to the method described above, and any method is usable thatenables the calculation of the reliability of the estimation resultsrelating to the subject to be estimated. The reliability of theestimation results relating to the subject to be estimated can bepresented to the user through the GUI described later, and whileconfirming the reliability through the GUI, the user can conduct anacceptability judgment (in step 324, 524) on the estimation resultsrelating to the learning sample (estimating sample) and an acceptabilityjudgment (in step 334, 534) on the estimation results relating to themeasurement subject.

Next, a method of estimation engine selection and/or weighting accordingto the present invention is described as an example below using FIG. 23.In this method, estimating of, for example, cross-sectional shapes orprocess parameters or the like, based on the above reliability that isanalytical results (1201) on the foregoing image characteristicquantities distribution, can be realized in a combination of pluralestimation engines by selecting one or more estimation engine (1602) andassigning a weighting value (W1, W2, . . . , Wn) to each estimationengine. For example, the estimation results of the above estimationengine are summed up by conducting the above weighting process tocalculate the estimated value mentioned above. The selection andweighting operations can be set using the GUI described later, and sincethe reliability of the image characteristic quantities, the reliabilityof the estimation engine, and the reliability of the estimation resultsare also displayed together through the GUI, these reliability valuescan be used to conduct image characteristic quantities and estimationengine adjustments, inclusive of the judgment on whether additionallearning is necessary. The user can also calculate the above reliabilityobtained after the above selections and weight adjustments have beenincorporated, and conduct readjustments while confirming the reliabilitythrough the GUI. The weight is used for cross-sectional shape or processparameter estimation in the performance process steps 350, 550. In thisway, estimation engine selection and weight adjustment become possible.

(GUI 1)

Next, a description is given below of an example of screen display of aGUI 1 in the learning process steps 300, 500 as shown in FIG. 24, theGUI 1 being connected to the image-processing/arithmetic processing unit407 of the semiconductor process estimation apparatus (cross-sectionalshape or process parameter estimation apparatus) according to thepresent invention. The GUI 1 makes it possible for the user to set upvarious detailed data for monitoring semiconductor processes bymonitoring cross-sectional shapes or process parameters. Thesemiconductor process estimation apparatus according to the presentinvention is characterized in that the apparatus has, as input GUI 1,all or part of items which enable selection of the functions shown inFIG. 24. These items are described below. The GUI 1 in this example isbroadly divided into two types of items: GUI items relating to learningdata setup (1700), and GUI items relating to reliability (1750) oflearning data.

First, GUI items on learning data setup (1700) are described by way ofexample. An item (1701) is used to specify a manufacturing process to beevaluated, and makes a lithographic process step (1702) and an etchingprocess step (1703) selectable.

An item (1712) is used to specify an evaluation mode, and makes itpossible to select cross-sectional shape estimation (1713) and processparameter estimation (1744). An item (1704) is used to specify the typeof pattern to be evaluated, and makes it possible to select design linewidth, design film thickness, and/or the like for a line pattern (1705),or to select a design hole diameter, a design aspect ratio, and/or thelike for a hole pattern (1706).

An item (1707) is used to specify image characteristic quantities to beused for estimation, and makes it possible to select the imagecharacteristic quantities to be used for estimation (e.g., MPPC imagecharacteristic quantities 1708 and textural information 1709).

An item (1725) is used to specify and graphically display desiredmeasurement points during cross-sectional shape estimation, and makes itpossible to specify height, width (1729) of the pattern to be evaluated,a shape (1726) of a corner of the pattern, a shape (1727) of a sidewallof the pattern, a shape (1728) of a footing portion, a tilt angle of asidewall, and so on.

Another item is used to specify desired measurement points, which are,for example, middle-CD (1721) and bottom-CD (1774). It is also possibleto specify estimated fluctuation ranges (1773, 1774) during thespecification of the measuring points.

Another item is related to learning setup for an estimation engine. Thisitem can be used to enter detailed design data for the imagecharacteristic quantities used during estimation, to select imagecharacteristic quantities (1732), and to set up the above weight (1731)for the selected image characteristic quantities.

Also, it is possible to select an estimation engine (1734), adjust eachparameter for an estimation engine (1735), and adjust a weight betweenestimation engines (1733).

The user can set all the above-described items. Also, if part of theitems is selected, certain items can be automatically selected.Selectable items can be learnt on the basis of a past measurementhistory, and automatic selection of typical measurement items is alsopossible. For example, if the selected evaluation process (1701) islithography (1702), the selected evaluation mode is cross-sectionalshape estimation (1713), and the selected type of pattern to beevaluated (1704) is the line pattern (1705), the MPPC characteristicquantities (1708) are selected automatically as the characteristicquantities to be used for estimation, bottom-CD (1722) is selected as anoutput evaluation index value, and only the k-NN method is used as theestimation engine. For example, 3 can be automatically selected as avalue of “k” in the k-NN method.

Furthermore, all or part of parameters to be used for estimation basedon, for example, selection results of image characteristic quantities orweight adjustment results of the image characteristic quantities orselection results of the estimation engine or weight adjustment resultsof the estimation engine, can be registered in database 408 for eachprocess step, product type, and process site of the subject to beestimated. When necessary, all or part of the above parameters can becalled from the database 408 and various kinds of estimations can alsobe set up.

Next, GUI items relating to reliability (1750) of the learning data aredescribed below. An item (1751) is used to display the above imagecharacteristic quantities information for each characteristic quantity.An item (1753) is a distribution of the image characteristic quantitiesand is displayed to confirm the distribution. An item (1755) makes itpossible to remove unnecessary learning samples (1755) on the basis ofthe reliability described later. In the present example, the estimatedfluctuation ranges (1770) can also be displayed together with the above.An item (1756) is used to select reliability data of imagecharacteristic quantities to be displayed, and makes it possible toselect, for example, sensitivity (1757), continuity (1758), separationlevel (1759), learning density (1760), and/or others of the imagecharacteristic quantities. It is also possible to enter theabove-mentioned threshold level (1761) for evaluating the reliability ofthe image characteristic quantities. An item (1762) is used to displaythe reliability of the image characteristic quantities. The reliabilitywith respect to cross-sectional shapes or process parameters can bedisplayed (1763). An item (1764) is used to display the reliability ofthe estimation engine. The reliability with respect to thecross-sectional shapes or process parameters can be displayed (1765). Anitem (1766) is used to display the reliability of the estimationresults. It is possible to display estimating results (1767) based onself-checking of estimation with the learning data (self-checking withthe estimation samples in the learning data), and to display reliability(1768) of the estimation results. The user can use information of thelearning data setup (1700) and reliability (1750) displayed through theGUI to set up appropriate learning data and estimation engines for thedesired type of estimation. The setup items displayed through the GUI inthe estimation apparatus are examples of the items that enable the userto set data. However, a method of setting estimation in detail to theuser in this manner makes it possible to meet various needs for processmanagement.

(GUI 2)

Next, a description is given below of an example of screen display of aGUI 2 in the performance process steps 350, 550 as shown in FIG. 25, theGUI 2 being connected to the image-processing/arithmetic processing unit407 of the semiconductor process estimation apparatus (cross-sectionalshape or process parameter estimation apparatus) according to thepresent invention. This output GUI 2 makes it possible for the user toconfirm detailed cross-sectional shape or process parameter estimationresults in detail and in a readily understandable format. The output GUI2 provides various items.

An item (1800) is used to display an evaluation process, and in thisitem, a process to be measured, such as lithography or etching, isdisplayed. Another item is used to display an evaluation mode, and inthis item, cross-sectional shape estimation (1802) or process parameters(1803) are displayed.

An item (1804) is used to specify the type of pattern to be evaluated.For example, a line pattern or a hole pattern is displayed in this item.An item (1820) is used to display calculation results on thecross-sectional shape being estimated. The calculated cross-sectionalshape can be displayed graphically, and various measurement points andmeasurement results can be displayed in an overlaid fashion. Forexample, pattern width (1808), a corner shape (1806), a sidewall shape(1807), a footing shape (1808), a sidewall tilt angle, and so on aredisplayed.

An item (1810) is used to display calculated data measurements. Formiddle-CD management (1811), for example, estimated data is displayedand reliability (1812) of estimation results is also displayed together.In addition, a plurality of estimation results can be displayed inarrayed form.

An item (1815) in which, when the estimation results that werecalculated from the pattern to be measured, and the reliability of theestimation results are calculated for a plurality of places on the wafersurface, distribution states of the estimation results and reliabilityon the wafer surface are displayed (1815). Any differences in data arerepresented as differences in display color or in brightness level(1816), and a distribution of these differences on the wafer surface isdisplayed. The measurement subject displayed in this item can bespecified (1814), and a plurality of index values can be selected from alist of evaluation indices (1813) and displayed. Time-varying changes inthe cross-sectional shape or process parameters obtained from thepattern to be measured are also displayed (1819).

In the present example, time is plotted on a horizontal axis and thecross-sectional shape or process parameters estimated are plotted on avertical axis (1820). The display items in the example areGUI-specifiable (1818), and a plurality of evaluation indices can beselected from the list and displayed (1817). Time-varying changes in thereliability (1821) of the estimation results can also be displayedtogether with the above data. This GUI is an example of a method ofestimating changes in time, and the user can monitor constantly changingpattern-forming parameters by monitoring, as described above,time-varying changes in estimation results and in the reliability of theestimation results.

The above-described display items in the estimation apparatus with GUIoutput are examples. However, since calculation results can be displayedto the user in detail in this fashion, it is possible to response tovarious process management needs and to supply process management statusinformation to the user in a readily understandable format by displayingeach item graphically.

According to the present invention, it is possible to calculate thecross-sectional shape of the pattern which has been formed in anexposure process or an etching process, from a SEM image withoutdestructing or damaging the pattern to be evaluated. Consequently, thistechnique makes highly efficient process management possible and hashigh industrial applicability.

The invention may be embodied in other specific forms without departingfrom the spirit or essential characteristics thereof. The presentembodiment is therefore to be considered in all respects as illustrativeand not restrictive, the scope of the invention being indicated by theappended claims, rather than by the following description, and allchanges that come within the meaning and range of equivalency of theclaims are therefore intended to be embraced therein.

1. A method for estimating a cross-sectional shape of a pattern, themethod comprising: a learning process step of acquiring learning datawhich includes SEM images of patterns having various cross-sectionalshapes, and selecting an estimation engine adapted to estimate thecross-sectional shape of the pattern; and a performance process step ofprocessing a SEM image obtained by imaging the pattern formed on asample by use of a SEM, calculating a characteristic quantity of the SEMimage, processing the calculated characteristic quantity using theselected estimation engine, and estimating the cross-sectional shape ofthe pattern formed on the sample; wherein, in the performance processstep, information on the estimated cross-sectional shape of the patternon the sample is output with information on reliability of estimationresults.
 2. The method for estimating a cross-sectional shape of apattern according to claim 1, wherein the learning process stepcomprises: a learning data registration step of using a SEM to acquire aSEM image group of a pattern group of various cross-sectional shapesbeforehand as a learning sample, then using another measurementapparatus to acquire an information group of the cross-sectional shapesof the pattern group, and registering, as learning data in a database,an association between the acquired SEM image group and the acquiredinformation group of the cross-sectional shapes; an image characteristicquantity calculation step of calculating a distribution group of imagecharacteristic quantities correlated to changes in three-dimensionalshapes of the pattern group, from the SEM image group within thelearning data which has been registered in the learning dataregistration step; a reliability calculation step of calculating any oneor a plurality of three kinds of reliability values, that is, areliability value for the image characteristic quantities within thelearning data, a reliability value for an estimation engine groupadapted to estimate the cross-sectional shapes, and a reliability valuefor a estimation result group obtained by the estimation of thecross-sectional shapes using the estimation engine group, based on thedistribution group of the image characteristic quantities that has beencalculated in the image characteristic quantity calculation step in anestimated fluctuation range of the cross-sectional shapes during amanufacturing process of forming the pattern on the sample; and adetermination step of determining the learning data and an estimationengine based on the reliability value or reliability values calculatedin the reliability calculation step, and registering the determinedlearning data and estimation engine in the database.
 3. The method forestimating a cross-sectional shape of a pattern according to claim 1,wherein the performance process step comprises: a SEM image acquisitionstep of acquiring a SEM image of the pattern formed on the sample; animage characteristic quantity calculation step of calculating an imagecharacteristic quantity based on the SEM image acquired from the patternon the sample in the SEM image acquisition step; a estimation step ofestimating the cross-sectional shape of the pattern on the sample,pursuant to the image characteristic quantity calculated in the imagecharacteristic quantity calculation step, and to the learning data andestimation engine determined in the learning process step; and areliability calculation step of calculating reliability of estimationresults obtained in the estimation step.
 4. The method for estimating across-sectional shape of a pattern according to claim 1, wherein in thelearning process step, the selected estimation engine is adapted to beadjustable on a screen.
 5. The method for estimating a cross-sectionalshape of a pattern according to claim 1, wherein when estimated in theperformance process step, the cross-sectional shape of the pattern onthe sample includes any one or more of a line width for each height, ashape of a crest portion, a tilt angle of a sidewall portion, a shape ofthe sidewall, a shape of a skirt-like portion, surface roughness of thepattern, a hole diameter of a contact hole, and depth of the contacthole.
 6. The method for estimating a cross-sectional shape of a patternaccording to claim 3, wherein in the performance process step,estimation results on the cross-sectional shape of the pattern that hasbeen estimated in the estimation step, and the reliability of theestimation results on the cross-sectional shape that has been calculatedin the reliability calculation step are evaluated, and results obtainedby the evaluation are displayed.
 7. The method for estimating across-sectional shape of a pattern according to claim 1, wherein in theperformance process step, when the cross-sectional shape is estimated,the plurality of estimation engines are used in combination.
 8. Themethod for estimating a cross-sectional shape of a pattern according toclaim 1, wherein in the performance process step, estimation results onthe cross-sectional shape of the pattern that has been estimated in theestimation step, and the reliability of the cross-sectional shapeestimation results that has been calculated in the reliabilitycalculation step are evaluated, and if results obtained by theevaluation are outside an allowable range, the evaluation results arefed back to a required manufacturing process site.
 9. The method forestimating a cross-sectional shape of a pattern according to claim 8,wherein any one or more of a focus position, dose rate, exposure time,baking temperature, baking time, and resist material used in an exposureprocess, or any one or more of an etching time, temperature in achamber, gas flow rate, and gas pressure used in an etching process isadjusted by feeding the evaluation results back to the requiredmanufacturing process site.
 10. An apparatus for estimating across-sectional shape of a pattern, the apparatus comprising: learningprocess means to acquire learning data which includes SEM images ofpatterns having various cross-sectional shapes, and select an estimationengine adapted to estimate the cross-sectional shape of the pattern; andperformance processing means to process a SEM image obtained by imagingthe pattern formed on a sample by use of a SEM, calculate acharacteristic quantity of the SEM image, process results obtained bythe calculation using the selected estimation engine, and estimate thecross-sectional shape of the pattern formed on the sample; wherein theperformance processing means outputs information on the estimatedcross-sectional shape of the pattern on the sample, along withinformation on reliability of estimation results.
 11. The apparatus forestimating a cross-sectional shape of a pattern according to claim 10,wherein the learning process means comprises: a learning dataregistration unit that acquires a SEM image group of a pattern group ofvarious cross-sectional shapes beforehand as a learning sample by use ofa SEM, acquires an information group of the cross-sectional shapes ofthe pattern group by use of another measurement apparatus, andregisters, as learning data in a database, an association between theacquired SEM image group and the acquired information group of thecross-sectional shapes; an image characteristic quantity calculationunit that calculates a distribution group of image characteristicquantities correlated to changes in three-dimensional shapes of thepattern group, from the SEM image group within the learning data whichhas been registered in the learning data registration unit; areliability calculation unit that calculates any one or a plurality ofthree types of reliability values, that is, a reliability value for theimage characteristic quantities within the learning data, a reliabilityvalue for an estimation engine group adapted to estimate thecross-sectional shapes, and a reliability value for a estimation resultgroup obtained during the estimation of the cross-sectional shapes usingthe estimation engine group, from the distribution group of the imagecharacteristic quantities that has been calculated by the imagecharacteristic quantity calculation unit in an estimated fluctuationrange of the cross-sectional shapes during a manufacturing process offorming the pattern on the sample; and a registration unit thatdetermines the learning data and an estimation engine from thereliability value or reliability values calculated by the reliabilitycalculation unit, and registers the determined learning data andestimation engine in the database.
 12. The apparatus for estimating across-sectional shape of a pattern according to claim 10, wherein theperformance processing means comprises: a SEM image acquisition unitthat acquires a SEM image of the pattern formed on the sample; an imagecharacteristic quantity calculation unit that calculates an imagecharacteristic quantity from the SEM image acquired from the pattern onthe sample by the SEM image acquisition unit; a cross-sectional shapeestimation unit that estimates the cross-sectional shape of the patternon the sample, pursuant to the image characteristic quantity calculatedby the image characteristic quantity calculation unit, and to thelearning data and estimation engine determined by the registration unit;and a reliability calculation unit that calculates reliability ofestimation results obtained by the cross-sectional shape estimationunit.
 13. The apparatus for estimating a cross-sectional shape of apattern according to claim 10, wherein in the learning process means,the selected estimation engine is adapted to be adjustable on a screen.14. The apparatus for estimating a cross-sectional shape of a patternaccording to claim 10, wherein when estimated by the performanceprocessing means, the cross-sectional shape of the pattern on the sampleincludes any one or more of a line width for each height, a shape of acrest portion, a tilt angle of a sidewall portion, a shape of thesidewall, a shape of a skirt-like portion, surface roughness of thepattern, a hole diameter of a contact hole, and depth of the contacthole.
 15. The apparatus for estimating a cross-sectional shape of apattern according to claim 12, wherein the performance processing meansevaluates estimation results on the cross-sectional shape of the patternthat has been estimated by the cross-sectional shape estimation unit,and the reliability of the estimation results of the cross-sectionalshape that has been calculated by the reliability calculation unit, andoutputs results obtained by the evaluation.
 16. The apparatus forestimating a cross-sectional shape of a pattern according to claim 12,wherein in the performance processing means, when the cross-sectionalshape is estimated, the plurality of estimation engines are used incombination.
 17. The apparatus for estimating a cross-sectional shape ofa pattern according to claim 10, wherein the performance processingmeans evaluates estimation results on the cross-sectional shape of thepattern that has been estimated by the cross-sectional shape estimationunit, and the reliability of the estimation results of thecross-sectional shape that has been calculated by the reliabilitycalculation unit, and if results obtained by the evaluation are outsidean allowable range, feeds back the evaluation results to a requiredmanufacturing process site.
 18. The apparatus for estimating across-sectional shape of a pattern according to claim 17, wherein anyone or more of a focus position, dose rate, exposure time, bakingtemperature, baking time, or resist material used in an exposure processor any one or more of an etching time, temperature in a chamber, gasflow rate, and gas pressure used in an etching process is adjusted byfeeding the evaluation results back to the required manufacturingprocess site.